timedAutomaton.ml 40.2 KB
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open Common
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open Batteries.Printf
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open Dbm
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open Uta

module type TIMED_AUTOMATON =
sig
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  module MDbm : BIG_IDBM
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  type timed_automaton
  type discrete_state
  type transition

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  module DS : Hashtbl.HashedType with type t = discrete_state

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  val clocks : timed_automaton -> string VarContext.t
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  val is_state_equal : discrete_state -> discrete_state -> bool
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  val initial_discrete_state : timed_automaton -> discrete_state
  (* does it belong here? If so, so does type for extended_state... *)
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  val initial_extended_state : timed_automaton -> discrete_state * MDbm.Dbm.t
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  val transitions_from : timed_automaton -> discrete_state ->
    (discrete_state * UDbm.Dbm.t * ((clock_t * int) list) * discrete_state) list
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  val transition_fields : timed_automaton -> transition ->
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    (discrete_state * UDbm.Dbm.t * ((clock_t * int) list) * discrete_state)
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  val guard_of_transition : timed_automaton -> transition -> UDbm.Dbm.t
  val invariant_of_discrete_state : timed_automaton -> discrete_state -> UDbm.Dbm.t
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  val is_urgent_or_committed : timed_automaton -> discrete_state -> bool
  val is_target : timed_automaton -> discrete_state -> bool
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  val lu_bounds : timed_automaton -> discrete_state -> Udbml.Carray.t * Udbml.Carray.t
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  val global_m_bounds : timed_automaton -> int array
  val global_m_invariant : timed_automaton -> UDbm.Dbm.t
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  (** print functions *)
  val print_discrete_state  : 'b BatIO.output -> timed_automaton -> discrete_state -> unit
  val print_transition : 'b BatIO.output -> timed_automaton -> transition -> unit
  val print_timed_automaton : 'b BatIO.output -> timed_automaton -> unit
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  val print_extended_state : 'b BatIO.output -> timed_automaton -> (discrete_state * MDbm.Dbm.t) -> unit
  val from_file : string -> string -> ?scale:int -> ?enlarge:int -> unit -> timed_automaton
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end

module type TIMED_GAME = 
sig
  include TIMED_AUTOMATON
  
  (* I am not convinced it is the better interface *)
  val is_controllable : timed_automaton -> edge -> bool
end

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module GenericUAutomaton (BDbm : BIG_IDBM) =
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struct
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  module MDbm = BDbm
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  module Dbm = BDbm.Dbm
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  (** In contrast with Uta.expression used in the parser, the variables here are indexed
   *  by unique integer identifiers.
   *)
  type expression =
    | Constant of int
    | Variable of int
    | Clock of int
    | Sum of expression * expression
    | Product of expression * expression
    | Substraction of expression * expression
    | Division of expression * expression

  type atomic_guard = 
    | GuardLeq of expression * expression
    | GuardLess of expression * expression
    | GuardGeq of expression * expression
    | GuardGreater of expression * expression
    | GuardEqual of expression * expression

  (** A guard is a conjunction of atomic guards *)
  type guard = atomic_guard list

  (** clocks updates *)
  type update = (int * expression) list

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  type simplechan = 
      SendChan of int
    | RecvChan of int
  

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  type edge = {
    edgeSource : int;
    edgeGuard : guard;
    edgeDiscGuard : guard;
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    edgeReset : (clock_t * int) list;
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    edgeDiscUpdate : update;
    edgeTarget : int;
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    edgeSync : simplechan option;
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    edgeProc : int; (* proc id *)
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    edgeControllable : bool
  }
  and location = {
    locId : int;
    mutable locName : string;
    locCommitted : bool;
    locUrgent : bool;
    locInvar : guard;
    locEdges : edge list;
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    locProc : int; (* proc id *)
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  }
  and process = {
    procName : string;
    procId : int;
    procLocations : location array;
    procInitLoc : int;
  }
  type discrete_state = {
    stateLocs : location array;
    stateVars : int array;
  }

  type transition = InternalTrans of discrete_state * edge
                  | SyncTrans of discrete_state * edge * edge

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  module LocHashtbl = Hashtbl.Make(
    struct
      type t = location array

      let equal a1 a2 =
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        let rec aux a b n =
          if (a.(n).locId = b.(n).locId) then
            if (n > 0) then aux a b (n-1)
            else true
          else false
        in aux a1 a2 (Array.length a1 - 1)
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      let hash a =
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        Array.fold_right
          (fun x r -> r + x.locId + 0x9e3779b9 + (r lsl 6) + (r lsr 2))
          a 0
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    end
  )

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  (** A succinct version of the above to be used in hash tables *)
  type _succinct_transition = int array * guard

  module GuardHashtbl = Hashtbl.Make(
    struct
      type t = _succinct_transition

      let equal x y = x = y

      let hash (a,b) =
        Array.fold_right
          (fun x r -> r + x + 0x9e3779b9 + (r lsl 6) + (r lsr 2))
          a (Hashtbl.hash b)
    end
  )
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  type timed_automaton = { 
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    procs : process array; (* forall i: procs.(i).procId = i *)
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    clocks : string VarContext.t;
    vars : string VarContext.t;
    init : discrete_state;
    mutable query : query;
    mutable lowerLU : int array array array;
    mutable upperLU : int array array array;
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    guards_tbl : UDbm.Dbm.t GuardHashtbl.t;
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    invars_tbl : UDbm.Dbm.t LocHashtbl.t;
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    lubounds_tbl : (Udbml.Carray.t * Udbml.Carray.t) LocHashtbl.t;
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  }
  

  (********** PRINTING AUXILIARY FUNCTIONS **********)
  let rec string_of_exp ta e = 
    let string_of_exp = string_of_exp ta in
    (function
      | Constant c -> sprintf "%d" c 
      | Variable(id) -> VarContext.var_of_index ta.vars id
      | Clock(id) ->  VarContext.var_of_index ta.clocks id
      | Product(e1,e2) ->
        sprintf "%s * %s" (string_of_exp e1)
          (string_of_exp e2)
      | Sum(e1,e2) ->
        sprintf "(%s + %s)" (string_of_exp e1)
          (string_of_exp e2)
      | Division(e1,e2) ->
        sprintf "%s / %s" (string_of_exp e1)
          (string_of_exp e2)
      | Substraction(e1,e2) ->
        sprintf "(%s - %s)" (string_of_exp e1)
          (string_of_exp e2)
    ) e


  let string_of_atomic_guard ta = 
    let string_of_exp = string_of_exp ta in
    function
    |  GuardLeq(v,exp) ->
      sprintf "%s <= %s" (string_of_exp v)(string_of_exp exp)
    | GuardLess(v,exp) ->
      sprintf "%s < %s" (string_of_exp v)(string_of_exp exp)
    | GuardGeq(v,exp)->
      sprintf "%s >= %s" (string_of_exp v)(string_of_exp exp)
    | GuardGreater(v,exp)->
      sprintf "%s > %s" (string_of_exp v) (string_of_exp exp)
    | GuardEqual(v,exp)->
      sprintf "%s == %s" (string_of_exp v) (string_of_exp exp)


  let xml_string_of_atomic_guard ta = 
    let string_of_exp = string_of_exp ta in       
    function
    |  GuardLeq(v,exp) ->
      sprintf "%s &lt;= %s" (string_of_exp v)(string_of_exp exp)
    | GuardLess(v,exp) ->
      sprintf "%s &lt; %s" (string_of_exp v)(string_of_exp exp)
    | GuardGeq(v,exp)->
      sprintf "%s &gt;= %s" (string_of_exp v)(string_of_exp exp)
    | GuardGreater(v,exp)->
      sprintf "%s &gt; %s" (string_of_exp v) (string_of_exp exp)
    | GuardEqual(v,exp)->
      sprintf "%s == %s" (string_of_exp v) (string_of_exp exp)


  let rec string_of_guard ta = 
    function
    | [] -> ""
    | [x] -> string_of_atomic_guard ta x
    | x :: y :: l -> 
      ((string_of_atomic_guard ta x) ^ " && ")
      ^ (string_of_guard ta (y::l))


  let rec xml_string_of_guard ta =
    function
    | [] -> ""
    | [x] -> xml_string_of_atomic_guard ta x
    | x :: y :: l -> 
      ((xml_string_of_atomic_guard ta x) ^ " &amp;&amp; ")
      ^ (xml_string_of_guard ta (y::l))


  let string_of_updates ta ups = 
    let ups_str = 
      List.map (fun (var,exp) -> sprintf "%s = %s" (VarContext.var_of_index ta.vars var) (string_of_exp ta exp)) ups in
    String.concat ", " ups_str

    
  let string_of_state ta state =
    let out = Buffer.create 50 in 
    Array.iter (fun loc -> Buffer.add_string out loc.locName;
                 Buffer.add_string out " ") state.stateLocs;
    if (Array.length state.stateVars > 0 ) then (
      Buffer.add_string out "\n";
      Array.iteri (fun i v ->
          let name = VarContext.index2var ta.vars i in
          Buffer.add_string out (sprintf "%s = %d, " name v)) state.stateVars;
    );
    (*    Buffer.add_string out "\n";*)
    Buffer.contents out

    
  let string_of_edge ta edge = 
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    let proc = ta.procs.(edge.edgeProc) in
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    let resetnames = 
      let out = Buffer.create 100 in
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      List.iter 
        (fun (cl, _) -> 
           let name = VarContext.index2var ta.clocks cl in
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           Buffer.add_string out name; 
           Buffer.add_string out " ") 
        edge.edgeReset;
      Buffer.contents out
    in
    let sync = match edge.edgeSync with 
      |None -> ""
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      |Some(SendChan(c)) -> (string_of_int c)^"!"
      |Some(RecvChan(c)) -> (string_of_int c)^"?"
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    in
    let discguardstr = string_of_guard ta edge.edgeDiscGuard in
    let guardstr = string_of_guard ta edge.edgeGuard in
    sprintf "%s%s -> %s \tDiscGuard: %s \tDiscUpdate: %s \tGuard: %s \tResets:%s \tSync:%s" 
      (if (edge.edgeControllable) then "" else "[E]")
      (proc.procLocations.(edge.edgeSource).locName)
      (proc.procLocations.(edge.edgeTarget).locName)
      discguardstr
      (string_of_updates ta edge.edgeDiscUpdate)
      guardstr
      resetnames
      sync
  (*
    sprintf "Edge:\n Target: %s.%s\n\tDiscGuard: %s\n\tDiscUpdate: %s\n\tGuard: %s\n\tResets:%s\n\tSync:%s\n" 
            proc.procName
            (proc.procLocations.(edge.edgeTarget).locName)
            discguardstr
            (string_of_updates ta edge.edgeDiscUpdate)
            guardstr
            resetnames
            sync
     *)

  
  let string_of_location ta loc =
    let out = Buffer.create 128 in
    let utter = Buffer.add_string out in
    utter (sprintf "Location %d: %s "loc.locId loc.locName);
    if (loc.locCommitted) then
      utter "committed ";
    utter (string_of_guard ta loc.locInvar);
    utter "\n";
    utter (sprintf "Has %d edges:\n" (List.length loc.locEdges));
    let edgestrlist = (List.map (string_of_edge ta) loc.locEdges) in
    utter (String.concat "\n" edgestrlist);
    utter "\n";
    Buffer.contents out


  let string_of_process ta proc = 
    let out = Buffer.create 1000 in
    let utter = Buffer.add_string out in
    utter (sprintf "Process(%d): %s\n"  proc.procId proc.procName);
    Array.iter (fun loc -> utter (string_of_location ta loc)) proc.procLocations;
    utter (sprintf "Initial location id: %d\n" proc.procInitLoc);
    Buffer.contents out


  let string_of_transition ta tr =
    let buf = Buffer.create 128 in
    let out = Buffer.add_string buf in
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    let proc_name e = ta.procs.(e.edgeProc).procName in
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    match tr with 
      InternalTrans(state,e) ->
      out (sprintf "From global state: %s\n" (string_of_state ta state));
      out (string_of_edge ta e);
      Buffer.contents buf
    | SyncTrans(state,e1,e2) ->
      out (sprintf "Synchronized Transition btw Processes: %s - %s\n Source: %s\n" (proc_name e1) (proc_name e2)
             (string_of_state ta state));
      out "Sync:\n";
      out (string_of_edge ta e1);
      out "\n";
      out (string_of_edge ta e2);
      Buffer.contents buf


  (********** OTHER AUXILIARY FUNCTIONS **********)
    
  let rec eval_disc_exp ta vars exp =
    try
      let k = 
        (match exp with
         | Constant c -> c
         | Variable(id) -> 
           if ( id < 0 || id >= Array.length vars ) then
             failwith (sprintf "Var index %d out of bounds (%d)" id (Array.length vars));
           vars.(id)
         | Clock(id) ->raise Found
         | Product(e1,e2) -> (eval_disc_exp ta vars e1) * (eval_disc_exp ta vars e2)
         | Sum(e1,e2) -> (eval_disc_exp ta vars e1) + (eval_disc_exp ta vars e2)
         | Division(e1,e2) -> (eval_disc_exp ta vars e1) / (eval_disc_exp ta vars e2)
         | Substraction(e1,e2) -> (eval_disc_exp ta vars e1) - (eval_disc_exp ta vars e2)
        ) in
      (*
      eprintf "%s -----> %d\n" (string_of_exp ta exp) k;
       *)
      k
    with Found ->
      failwith ("Discrete expression contains clock: " ^ (string_of_exp ta exp)); 
       | e -> raise e

       
  let source_location_of_edge ta edge =
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    ta.procs.(edge.edgeProc).procLocations.(edge.edgeSource)
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  let eval_disc_guard ta state guard =
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    let rec aux_eval t v = function
      | [] -> true
      | GuardLeq(e1,e2) :: l ->
          if (    (eval_disc_exp t v e1)
              <=  (eval_disc_exp t v e2)) then
                aux_eval t v l
          else
            false
      | GuardLess(e1,e2) :: l ->
          if (    (eval_disc_exp t v e1)
              <   (eval_disc_exp t v e2)) then
                aux_eval t v l
          else
            false
      | GuardGeq(e1,e2) :: l ->
          if (    (eval_disc_exp t v e1)
              >=  (eval_disc_exp t v e2)) then
                aux_eval t v l
          else
            false
      | GuardGreater(e1,e2) :: l ->
          if (    (eval_disc_exp t v e1)
              >   (eval_disc_exp t v e2)) then
                aux_eval t v l
          else
            false
      | GuardEqual(e1,e2) :: l ->
          if (    (eval_disc_exp t v e1)
              =   (eval_disc_exp t v e2)) then
                aux_eval t v l
          else
            false
    in aux_eval ta state.stateVars guard
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  let _guard_to_dbm ta state g =
    let nclocks = VarContext.size ta.clocks in
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    let dbm = UDbm.Dbm.create nclocks in
    UDbm.Dbm.set_init dbm;
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    let aux = function
      | GuardLeq(Clock(c), e) ->
          let k = eval_disc_exp ta state e in
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          UDbm.Dbm.constrain dbm (c, 0, (k, Udbml.Basic_types.DBM_WEAK))
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      | GuardLess(Clock(c), e) ->
        let k = eval_disc_exp ta state e in
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        UDbm.Dbm.constrain dbm (c, 0, (k, Udbml.Basic_types.DBM_STRICT))
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      | GuardGeq(Clock(c), e) ->
        let k = eval_disc_exp ta state e in
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        UDbm.Dbm.constrain dbm (0, c, (-k, Udbml.Basic_types.DBM_WEAK))
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      | GuardGreater(Clock(c), e) ->
        let k = eval_disc_exp ta state e in
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        UDbm.Dbm.constrain dbm (0, c, (-k, Udbml.Basic_types.DBM_STRICT))
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      | GuardEqual(Clock(c), e) ->
        let k = eval_disc_exp ta state e in
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        UDbm.Dbm.constrain dbm (0, c, (-k, Udbml.Basic_types.DBM_WEAK));
        UDbm.Dbm.constrain dbm (c, 0, (k, Udbml.Basic_types.DBM_WEAK))
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      | _ as e -> failwith (sprintf "Bad Guard: %s" (string_of_guard ta [e]))
    in
    List.iter aux g;
    dbm


  let is_committed state =
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    let rec aux ar n =
      if (ar.(n).locCommitted) then true
      else if (n > 0) then
        aux ar (n-1)
      else false
    in aux state.stateLocs (Array.length state.stateLocs - 1)
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  let _copy_state state = 
    { stateVars = Array.copy state.stateVars;
      stateLocs = Array.copy state.stateLocs}


  (** Apply discrete update of edge to state, result written in state' *)
  let _apply_edge ta state edge state' =
    let aux = fun (id,e) -> 
      state'.stateVars.(id) <- eval_disc_exp ta state.stateVars e
    in
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    state'.stateLocs.(edge.edgeProc) <- ta.procs.(edge.edgeProc).procLocations.(edge.edgeTarget);
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    List.iter aux edge.edgeDiscUpdate



  (********** TIMED_AUTOMATON interface **********)
  let clocks ta = ta.clocks

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  let hash_discrete_state s =
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    let tmp = Array.fold_right
      (fun x r -> r + x.locId + 0x9e3779b9 + (r lsl 6) + (r lsr 2))
      s.stateLocs 0
    in Array.fold_right
      (fun x r -> r + x + 0x9e3779b9 + (r lsl 6) + (r lsr 2))
      s.stateVars tmp
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  let is_state_equal s t =
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    let rec aux_loc a b n =
      if (n < 0) then true else
      if (a.(n).locId = b.(n).locId) then
        if (n > 0) then
          aux_loc a b (n-1)
        else true
      else false
    in
    let rec aux_var a b n =
      if (n < 0) then true else
      if (a.(n) = b.(n)) then
        if (n > 0) then
          aux_var a b (n-1)
        else true
      else false
    in
    (aux_loc s.stateLocs t.stateLocs (Array.length s.stateLocs - 1))
    &&
    (aux_var s.stateVars t.stateVars (Array.length s.stateVars - 1))
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  module DS = struct
    type t = discrete_state
    let equal = is_state_equal
    let hash = hash_discrete_state
  end

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  let initial_discrete_state ta = ta.init

  let invariant_of_discrete_state ta state =
    try
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      LocHashtbl.find ta.invars_tbl state.stateLocs
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    with Not_found ->
      let glob_inv =
        Array.fold_left (fun acc loc -> loc.locInvar @ acc ) [] state.stateLocs in
      let inv = _guard_to_dbm ta state.stateVars glob_inv in
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      LocHashtbl.add ta.invars_tbl state.stateLocs inv;
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      inv
       | _ as e -> raise e

  let initial_extended_state ta =
    let dim = (VarContext.size (clocks ta)) in
    let z = Dbm.create dim in
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    Dbm.set_zero z;
    (ta.init, z)
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  let _transitions_from ta state = 
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    let committed = is_committed state in
    let transq = Queue.create () in
    (* Queue of synchronizing edges *)
    let rchan = Queue.create () in
    let schan = Queue.create () in
    let nproc = Array.length ta.procs in
    for i = 0 to nproc - 1 do
      let loc = state.stateLocs.(i) in
      let add_single = not committed || loc.locCommitted in
      List.iter
        (fun edge ->
          if (eval_disc_guard ta state edge.edgeDiscGuard) then
            (match edge.edgeSync with
              | Some (SendChan(c)) ->
                  Queue.add (c, edge) schan
              | Some (RecvChan(c)) ->
                  Queue.add (c, edge) rchan
              | None ->
                  if (add_single) then
                    Queue.add (InternalTrans (state, edge)) transq
            )
        ) loc.locEdges
    done;
    Queue.iter
      (fun (rname, redge) ->
        Queue.iter
          (fun (sname, sedge) ->
            (* Sync if same channels are used by different processes *)
            if (rname = sname && redge.edgeProc <> sedge.edgeProc) then (
              (* and if state not committed or one of the participating states is *)
              let sloc = source_location_of_edge ta sedge in
              let rloc = source_location_of_edge ta redge in
              if (not committed || sloc.locCommitted || rloc.locCommitted) then
                Queue.add (SyncTrans (state, redge, sedge)) transq
            )
          ) schan
      ) rchan;
    Queue.fold (fun l tr -> tr :: l) [] transq

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  let guard_of_transition ta tr = 
    let to_succinct = function
      |InternalTrans(s,e) -> (s.stateVars,e.edgeGuard)
      |SyncTrans(s,e1,e2) -> (s.stateVars,List.rev_append e1.edgeGuard e2.edgeGuard)
    in
    let (vars,succ_guard) as str = to_succinct tr in
    try 
      GuardHashtbl.find ta.guards_tbl str
    with Not_found ->
      let g = _guard_to_dbm ta vars succ_guard in
      GuardHashtbl.add ta.guards_tbl str g;
      g
      | _ as e -> raise e

  let transition_fields ta tr = match tr with
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    | InternalTrans(state, e) ->
        let state' = _copy_state state in
        _apply_edge ta state e state';
        (state,
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         guard_of_transition ta tr,
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         e.edgeReset,
         state')
    | SyncTrans(state, e1, e2) ->
        let state' = _copy_state state in
        _apply_edge ta state e1 state';       
        _apply_edge ta state e2 state';
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        let g = guard_of_transition ta tr in
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        (state, g, e1.edgeReset @ e2.edgeReset, state')
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  let transitions_from ta state =
    List.map (fun tr -> transition_fields ta tr) (_transitions_from ta state)

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  let is_urgent_or_committed ta state =
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    let rec aux ar n =
      if (ar.(n).locCommitted || ar.(n).locUrgent) then true
      else if (n > 0) then
        aux ar (n-1)
      else false
    in aux state.stateLocs (Array.length state.stateLocs - 1)
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  let is_target ta state =
    let rec eval = function
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      | AtomicQuery(s) ->
          Array.fold_left (fun ac -> fun loc -> ac || loc.locName = s) false state.stateLocs
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      | OrQuery(p1,p2) -> (eval p1) || (eval p2)
      | AndQuery(p1,p2) -> (eval p1) && (eval p2)
      | NotQuery(p) -> not (eval p)
    in
    match ta.query with
      EmptyQuery -> true
    | ReachQuery(pq) -> eval pq

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  let lu_bounds ta state =
    try
      LocHashtbl.find ta.lubounds_tbl state.stateLocs
    with Not_found ->
      let mymax (x:int) (y:int) =
        if (x < y) then y else x
      in
      let nclocks = VarContext.size ta.clocks in
      let lbounds = Array.make nclocks (-Dbm.infty) in
      let ubounds = Array.make nclocks (-Dbm.infty) in
      lbounds.(0) <- 0;
      ubounds.(0) <- 0;
      let nprocs = Array.length state.stateLocs in
      for iproc = 0 to nprocs - 1 do
        let iloc = state.stateLocs.(iproc).locId in
        for cl = 0 to nclocks - 1 do
          lbounds.(cl) <- mymax lbounds.(cl) ta.lowerLU.(iproc).(iloc).(cl);
          ubounds.(cl) <- mymax ubounds.(cl) ta.upperLU.(iproc).(iloc).(cl);
        done;
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      done;
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      let (lar, uar) = (Udbml.Carray.to_c lbounds nclocks, Udbml.Carray.to_c ubounds nclocks) in
      LocHashtbl.add ta.lubounds_tbl state.stateLocs (lar, uar);
      (lar, uar)
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  let global_m_bounds ta =
    let nclocks = VarContext.size (clocks ta) in
    let result = Array.make nclocks (-Dbm.infty) in
    result.(0) <- 0;
    for cl = 0 to nclocks-1 do
      for i = 0 to (Array.length ta.lowerLU) - 1 do
        for j = 0 to (Array.length ta.lowerLU.(i)) - 1 do
          let mymax (x:int) (y:int) =
            if (x < y) then y else x
          in
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          result.(cl) <- mymax result.(cl) ta.lowerLU.(i).(j).(cl);
          result.(cl) <- mymax result.(cl) ta.upperLU.(i).(j).(cl)
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        done
      done;
    done;
    result

  let global_m_invariant ta =
    let marray = global_m_bounds ta in
    let inv_guard = ref [] in
    for i = 0 to (Array.length marray)-1 do
      inv_guard := (GuardLeq (Clock i, Constant marray.(i))) :: !inv_guard
    done;
    _guard_to_dbm ta ta.init.stateVars !inv_guard
    
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  (** print functions *)
  let print_discrete_state chan ta state =
    fprintf chan "%s\n" (string_of_state ta state)
  
  let print_transition chan ta trans = 
    fprintf chan "%s\n" (string_of_transition ta trans)

  let print_timed_automaton chan ta =
    fprintf chan "Timed automaton with %d clocks and %d processes\n"
      (VarContext.size ta.clocks) (Array.length ta.procs);
    Array.iter (fun proc -> fprintf chan "%s\n-----\n" (string_of_process ta proc)) ta.procs
 
  let print_extended_state chan ta (state,dbm) =
    fprintf chan "%s " (string_of_state ta state);
    fprintf chan "%s " (Dbm.to_string dbm)

  (********** LOADING FUNCTIONS **********)
  
  (** This is pretty much a direct translation from LocalLUNormalizer class of Verifix.
      @return a pair (lower,upper) corresponding to L and U values, three-dimensional arrays indexed by  process, location, and clock
      *)
  let _make_lu_table ta = 
    let nclocks = VarContext.size ta.clocks in
    let maketable () = 
      Array.map (fun proc -> 
          Array.map (fun loc ->
              Array.init nclocks (fun c -> -Dbm.infty)
            ) proc.procLocations
        ) ta.procs
    in
    let upper = maketable () in
    let lower = maketable () in
    let process iproc iloc g = 
      let aux = function
        | GuardLeq(Clock(l),Constant(r)) ->
          upper.(iproc).(iloc).(l) <- max upper.(iproc).(iloc).(l) r
        | GuardLess(Clock(l),Constant(r)) ->
          upper.(iproc).(iloc).(l) <- max upper.(iproc).(iloc).(l) r
        | GuardEqual(Clock(l),Constant(r)) ->
          upper.(iproc).(iloc).(l) <- max upper.(iproc).(iloc).(l) r;
          lower.(iproc).(iloc).(l) <- max lower.(iproc).(iloc).(l) r
        | GuardGreater(Clock(l),Constant(r)) ->
          lower.(iproc).(iloc).(l) <- max lower.(iproc).(iloc).(l) r
        | GuardGeq(Clock(l),Constant(r)) ->
          lower.(iproc).(iloc).(l) <- max lower.(iproc).(iloc).(l) r
        | _ -> failwith "Cannot compute lu bounds: Guards not in normal form."
      in
      List.iter aux g
    in
    let close bounds iproc proc = 
      let stable = ref false in
      while (not !stable) do
        stable := true;
        Array.iter (fun loc -> 
            List.iter (fun edge ->
                let source = edge.edgeSource in
                let target = edge.edgeTarget in
                let sourceBnd = bounds.(iproc).(source) in
                let targetBnd = bounds.(iproc).(target) in
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                for j = 1 to nclocks - 1 do
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                  if (not (List.exists (fun (cl,_) -> j = cl) edge.edgeReset)) then (
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                    if (targetBnd.(j) > sourceBnd.(j) ) then(
                      sourceBnd.(j) <- targetBnd.(j);
                      stable := false
                    )                                     
                  )
                done
              ) loc.locEdges
          ) proc.procLocations
      done;
    in
    Array.iteri (fun iproc proc -> 
        (* Initialize *)
        Array.iteri (fun iloc loc ->
            List.iter (fun edge ->
                process iproc iloc edge.edgeGuard) 
              loc.locEdges;
            process iproc iloc loc.locInvar
          ) proc.procLocations;
        (* Close *)
        close lower iproc proc;
        close upper iproc proc;
      ) ta.procs;
    (lower,upper)


  (** Constructs a timed_automaton. The constructor function is parameterized
   *  by guard_of_transition and invariant_of_discrete_state so that we can 
   *  instantiate it for other kinds of automata (enlarged automata below)
   *  in modules extending the current one.
       @param sys parsed system (Uta.system)
       @param scale scales all constants by scale
       @param enlarge enlarges all constants by enlarge (after having scaled)
       @param (guard_of_transition,invariant_of_discrete_state)
      *)
  let make_ta (guard_of_transition, invariant_of_discrete_state) sys scale enlarge = 
    let templates = sys.sysTemplates in 
    (** Variable and clock contexts have initially keys of type (p,name)
     * where p is process option (None for global variables),
     * and name the name of the variable. *)
    let varcont = VarContext.create () in
    let var_init_values = Hashtbl.create 10 in
    let const_values = Hashtbl.create 10 in
    let clockcont = VarContext.create () in
    VarContext.add clockcont (None,"0");
    let constcont = VarContext.create () in
    (* Function to register global clocks and variables *)
    let register_vars tmp (clocks,vars) = 
      List.iter (fun cl -> 
          try VarContext.add clockcont (tmp,cl) 
          with Var_already_defined -> 
            eprintf "Variable %s is already defined\n" cl;
            failwith "Error"
             | _ as e ->
               raise e
        ) clocks;
      List.iter (fun var -> 
          try 
            match var with
              Var(id,v) ->
              VarContext.add varcont (tmp,id);
              let index = VarContext.index_of_var varcont (tmp,id) in
              Hashtbl.add var_init_values index v
            | ConstVar(id,v) ->
              VarContext.add constcont (tmp,id);
              let index = VarContext.index_of_var constcont (tmp,id) in                     
              Hashtbl.add const_values index v
          with Var_already_defined ->
            eprintf "Variable %s is already defined\n" (name_of_var var);
            failwith "Error"
             | _ as e ->
               raise e
        ) vars
    in
    (* Register variables: first global ones then local ones *)
    register_vars None (sys.sysClocks, sys.sysVars);
    List.iter (fun tmp -> register_vars (Some tmp) (tmp.tempClocks, tmp.tempVars) ) templates;
    let nvars = (VarContext.size varcont) in
    let is_clock tmp var = 
      if (VarContext.mem clockcont (Some tmp,var)) then
        true
      else if (VarContext.mem clockcont (None,var)) then
        true
      else 
        false
    in
    let get_clock_id tmp var = 
      if (VarContext.mem clockcont (Some tmp,var) ) then
        VarContext.index_of_var clockcont (Some tmp,var)
      else
        VarContext.index_of_var clockcont (None,var)
    in
    (* Convert the given Uta.expression inside the template tmp to the local exp type
       by replacing variable names by their integer identifiers. Also instantiates constants
       and partially evaluates the arithmetic operations  *)
    let convert_exp tmp exp = 
      let rec eval = function
        | Uta.Constant(c) -> Constant(c)
        | Uta.Variable(name) -> 
          (* We first check if the variable is a constant *)
          if (VarContext.mem constcont (Some tmp,name) ) then
            (* Is it a local constant? *)
            let varid = VarContext.index_of_var constcont (Some tmp,name) in
            Constant(Hashtbl.find const_values varid)
          else if (VarContext.mem constcont (None,name)) then
            (* Is it a global constant ? *)
            let varid = VarContext.index_of_var constcont (None,name) in
            Constant(Hashtbl.find const_values varid)
          else if (VarContext.mem varcont (Some tmp,name)) then
            (* Is it a local variable? *)
            let varid = VarContext.index_of_var varcont (Some tmp,name) in
            Variable(varid)
          else if (VarContext.mem varcont (None,name)) then
            (* Is it a global variable? *)
            let varid = VarContext.index_of_var varcont (None,name) in
            Variable(varid)
          else if (VarContext.mem clockcont (Some tmp, name) ) then
            (* Local clock *)
            let varid = VarContext.index_of_var clockcont (Some tmp,name) in
            Clock(varid)            
          else if (VarContext.mem clockcont (None, name) ) then
            (* Global clock *)
            let varid = VarContext.index_of_var clockcont (None,name) in
            Clock(varid)    
          else (
            eprintf "Printing final VarContext\n";
            VarContext.iter 
              (fun (t,name) ind ->
                 let scope = match t with None -> "None" | Some tmp -> tmp.tempName
                 in
                 eprintf "\t%d <%s> : %s\n" ind  name scope
              ) varcont;
            printf "%b\n" (VarContext.mem varcont (Some tmp, name));
            failwith (sprintf "Undefined variable <%s>" name)
          )
        | Uta.Sum(e1,e2)  ->
          let ne1 = eval e1 in
          let ne2 = eval e2 in
          (match (ne1,ne2) with
             Constant(v1), Constant(v2) -> Constant(v1 + v2)
           | _ -> Sum(ne1,ne2)
          )
        | Uta.Subtraction(e1,e2)  ->
          let ne1 = eval e1 in
          let ne2 = eval e2 in
          (match (ne1,ne2) with
             Constant(v1), Constant(v2) -> Constant(v1 - v2)
           | _ -> Substraction(ne1,ne2)
          )
        | Uta.Product(e1,e2)  ->
          let ne1 = eval e1 in
          let ne2 = eval e2 in
          (match (ne1,ne2) with
             Constant(v1), Constant(v2) -> Constant(v1 * v2)
           | _ -> Product(ne1,ne2)
          )
        | Uta.Division(e1,e2)  ->
          let ne1 = eval e1 in
          let ne2 = eval e2 in
          (match (ne1,ne2) with
             Constant(v1), Constant(v2) -> Constant(v1 / v2)
           | _ -> Division(ne1,ne2)
          )
      in
      eval exp
    in
    let convert_guard tmp g  =
      let convert_atomic_guard = function
        | Uta.GuardLeq(e1,e2) -> GuardLeq(convert_exp tmp e1, convert_exp tmp e2)
        | Uta.GuardLess(e1,e2) -> GuardLess(convert_exp tmp e1, convert_exp tmp e2)
        | Uta.GuardGeq(e1,e2) -> GuardGeq(convert_exp tmp e1, convert_exp tmp e2)
        | Uta.GuardGreater(e1,e2) -> GuardGreater(convert_exp tmp e1, convert_exp tmp e2)
        | Uta.GuardEqual(e1,e2) -> GuardEqual(convert_exp tmp e1, convert_exp tmp e2)
      in
      (* Make sure clock guards have the form Guard*(Clock(cl),Constant(r)) *)
      let normalize_atomic_guard = function
        | GuardLeq(_ as k,Clock(cl)) ->
          GuardGeq(Clock(cl),k)
        | GuardLess(_ as k,Clock(cl)) ->
          GuardGreater(Clock(cl),k)
        | GuardGeq(_ as k,Clock(cl)) ->
          GuardLeq(Clock(cl),k)
        | GuardGreater(_ as k,Clock(cl)) ->
          GuardLess(Clock(cl),k)
        | GuardEqual(_ as k,Clock(cl)) ->
          GuardEqual(Clock(cl),k)
        | e -> e
      in
      let aux ag = 
        normalize_atomic_guard (convert_atomic_guard ag)
      in
      let g = List.map aux g in
      g
    in
    (** Instantiate constants inside updates *)
    let convert_update tmp up = 
      List.map (fun (var,exp) -> 
          let varid = 
            if (VarContext.mem varcont (Some tmp,var)) then
              VarContext.index_of_var varcont (Some tmp,var)
            else                   
              VarContext.index_of_var varcont (None,var) 
          in
          (varid,convert_exp tmp exp)
        ) up
    in
    (** Get discrete guard from mixed guard *)
    let filter_disc_guard tmp g = 
      let filt_ag ag = 
        List.for_all (fun name -> not (is_clock tmp name)) (vars_of_atomic_guard ag)
      in
      List.filter filt_ag g
    in
    (** Get clock guard from mixed guard *)
    (* TODO Also check that there is no variable *)
    let filter_clock_guard tmp g = 
      let filt_ag ag = 
        List.exists (fun name -> (is_clock tmp name)) (vars_of_atomic_guard ag)
      in
      List.filter filt_ag g
    in
    (** Make clock reset set *)
    let clock_update tmp up =
      let reset = 
        (List.map (fun (name,_) -> get_clock_id tmp name)
           (List.filter (fun (var,_) -> is_clock tmp var) up))
        |>
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        (List.fold_left (fun l cl -> (cl, 0)::l) [])
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      in
      reset
    in
    (** scale all constants by scale and enlarge by enlarge*)
    let scale_and_enlarge_cguard g =
      let rec eval = function
        | Sum(e1,e2)  ->
          let ne1 = eval e1 in
          let ne2 = eval e2 in
          (match (ne1,ne2) with
             Constant(v1), Constant(v2) -> Constant(v1 + v2)
           | _ -> Sum(ne1,ne2)
          )
        | Substraction(e1,e2)  ->
          let ne1 = eval e1 in
          let ne2 = eval e2 in
          (match (ne1,ne2) with
             Constant(v1), Constant(v2) -> Constant(v1 - v2)
           | _ -> Substraction(ne1,ne2)
          )
        | Product(e1,e2)  ->
          let ne1 = eval e1 in
          let ne2 = eval e2 in
          (match (ne1,ne2) with
             Constant(v1), Constant(v2) -> Constant(v1 * v2)
           | _ -> Product(ne1,ne2)
          )
        | Division(e1,e2)  ->
          let ne1 = eval e1 in
          let ne2 = eval e2 in
          (match (ne1,ne2) with
             Constant(v1), Constant(v2) -> Constant(v1 / v2)
           | _ -> Division(ne1,ne2)
          )
        | e -> e
      in
      let s = Constant(scale) in
      let d = Constant(enlarge) in
      let scale_and_enlarge = function
        | GuardLeq(Clock(_) as e1,e2) -> [GuardLeq(e1,eval (Sum(Product(e2,s),d)))]
        | GuardLess(Clock(_) as e1,e2) -> [GuardLess(e1,eval (Sum(Product(e2,s),d)))]
        | GuardGreater(Clock(_) as e1,e2) -> [GuardGreater(e1,eval (Substraction(Product(e2,s),d)))]
        | GuardGeq(Clock(_) as e1,e2) -> [GuardGeq(e1,eval (Substraction(Product(e2,s),d)))]
        | GuardEqual(Clock(_) as e1,e2) ->
          let se2 = Product(e2,s) in
          [GuardGeq(e1,eval (Substraction(se2,d)));
           GuardLeq(e1,eval (Sum(se2,d)))
          ]
        | other ->
          failwith "Cannot enlarge non-normalized clock guard"
      in
      List.fold_left (fun acc ag -> (scale_and_enlarge ag)@acc) [] g
    in
    (* Convert the (template,string) VarContext.t  to string VarContext.t
       by prepending the process names to variables and clocks. 
       We will just extract these elements from the hash tables, along with their indices,
       so as to reinsert them in the same order in the new VarContext.
       These contexts are only for pretty printing and have no role in simulation
    *)
    let get_vc_elements vc = 
      Hashtbl.fold 
        (fun (tmp,name) index acc ->
           let prefix = match tmp with
               None -> ""
             | Some tmp -> tmp.tempName ^"."
           in
           let name = sprintf "%s%s" prefix name in
           (index,name) :: acc
        ) (VarContext.get_var2index vc) [] 
    in    
    let clist = List.sort compare (get_vc_elements clockcont) in
    let vlist = List.sort compare (get_vc_elements varcont) in
    let clocks = VarContext.create () in
    let vars = VarContext.create () in
    List.iter (fun (_,name) -> VarContext.add clocks name) clist;
    List.iter (fun (_,name) -> VarContext.add vars name) vlist;
    let disc_update tmp up =
      List.filter (fun (var,_) -> not (is_clock tmp var)) up
    in
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    (* Assign integer identifiers to channels.
     *)
    let chanids = Hashtbl.create 50 in
    let next_chan_id = ref 0 in
    let chan_to_id s =
      try Hashtbl.find chanids s 
      with Not_found -> (
        incr next_chan_id;
        Hashtbl.add chanids s !next_chan_id;
        !next_chan_id)
    in
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    (** Now we start making the timed automaton *)
    let make_proc id tmp = 
      (* Assign integer identifiers to locations by their locId's.
         We assign id i to the i-th location in the list (see below)
      *)
      let locids = Hashtbl.create 50 in
      List.iteri (fun i loc -> Hashtbl.add locids loc.Uta.locId i) tmp.tempLocations;
      let make_edge edge = 
        {
          edgeSource = Hashtbl.find locids edge.Uta.edgeSource;
          edgeTarget = Hashtbl.find locids edge.Uta.edgeTarget;
          edgeDiscGuard = convert_guard tmp (filter_disc_guard tmp edge.Uta.edgeGuard);
          edgeGuard = scale_and_enlarge_cguard
              (convert_guard tmp (filter_clock_guard tmp edge.Uta.edgeGuard));
          edgeReset = clock_update tmp edge.edgeUpdates;
          edgeDiscUpdate = convert_update tmp (disc_update tmp edge.edgeUpdates);
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          edgeSync = (match edge.Uta.edgeSync with
            | None -> None
            | Some(SendChan(s)) -> Some(SendChan(chan_to_id s))
            | Some(RecvChan(s)) -> Some(RecvChan(chan_to_id s)));
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          edgeProc = id;
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          edgeControllable = true;
        }
      in
      let make_loc loc = 
        let edges = 
          let e = List.filter
              (fun edge -> edge.Uta.edgeSource = loc.Uta.locId) tmp.tempEdges in
          List.map make_edge e                   
        in
        {
          locId = Hashtbl.find locids loc.Uta.locId;
          locName = if (loc.Uta.locName <> "") then loc.Uta.locName else loc.Uta.locId;
          locCommitted = loc.Uta.locCommitted;
          locUrgent = loc.Uta.locUrgent;
          locInvar = scale_and_enlarge_cguard (convert_guard tmp loc.Uta.locInvar);
          locEdges = List.rev edges;
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          locProc = id;
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        }
      in
      let locslist = List.map make_loc tmp.tempLocations in
      let locs = Array.of_list locslist in
      {
        procName = tmp.Uta.tempName;
        procId = id;
        procLocations = locs;
        procInitLoc = Hashtbl.find locids tmp.tempInitialLocation.locId;
      } 
    in
    let procs = Array.of_list (List.mapi make_proc templates) in
    (* Fill in the edgeProc and locProc fields in all locations and edges *)
    Array.iter (fun proc -> 
        Array.iter (fun loc -> 
            loc.locName <- proc.procName ^ "." ^ loc.locName;
          ) proc.procLocations
      )
      procs;
    let initLocs = Array.map (fun proc -> proc.procLocations.(proc.procInitLoc)) procs in
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    let initVars = Array.make nvars 0 in
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    for i = 0 to nvars-1 do
      initVars.(i) <- Hashtbl.find var_init_values i;
    done;
    let ta = {
      procs = procs;
      clocks = clocks;
      vars = vars;
      init = {stateLocs = initLocs; stateVars = initVars};
      query = EmptyQuery;
      lowerLU = [||];
      upperLU = [||];
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      guards_tbl = GuardHashtbl.create 1024;
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      invars_tbl = LocHashtbl.create 1024;
      lubounds_tbl = LocHashtbl.create 1024
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    }
    in 
    let (lower,upper) = _make_lu_table ta in
    ta.lowerLU <- lower;
    ta.upperLU <- upper;
    (** Check restrictions:
     * 1) No discrete variables in clock guards
     *    ( This restriction could actually be lifted
     *      by redefining the hash tables as a function
     *      from state = stateLocs * stateVars)
     *)
    let check_ta ta =
      let check_guard_no_discrete g = 
        let aux = function 
          |Variable(_) -> raise Found
          | _ -> ()
        in
        let atomic = function       
          | GuardLess(e1,e2) -> aux e1; aux e2
          | GuardLeq(e1,e2) -> aux e1; aux e2
          | GuardGeq(e1,e2) -> aux e1; aux e2
          | GuardGreater(e1,e2) -> aux e1; aux e2
          | GuardEqual(e1,e2) -> aux e1; aux e2
        in
        List.iter atomic g
      in
      (try
         ta.procs |> Array.iter (fun proc ->
             proc.procLocations |> 
             Array.iter (fun loc ->
                 check_guard_no_discrete loc.locInvar;
                 loc.locEdges |> List.iter (fun edge -> check_guard_no_discrete edge.edgeGuard)
               )
           ) 
       with Found -> failwith "We do not support discrete variables in clock guards"
          | _ as e -> raise e
      )
    in
    check_ta ta;
    ta


  let from_file tafile qfile ?scale:(scale=1) ?enlarge:(enlarge=0) () = 
    let pta  = UtaReader.nta_from_file (tafile) in
    let query = UtaReader.query_from_file qfile in
    let ta = make_ta (guard_of_transition, invariant_of_discrete_state) pta scale enlarge in
    ta.query <- query;
    ta
  
end