solver.ml 11.9 KB
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(*-----------------------------------------------------------------------
** Copyright (C) 2001 - Verimag.
** This file may only be copied under the terms of the GNU Library General
** Public License 
**-----------------------------------------------------------------------
**
** File: solver.ml
** Main author: jahier@imag.fr
*)

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open List
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open Formula
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open Env_state
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open Util
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(****************************************************************************)
	  
let (formula_list_to_conj: formula list -> formula) =
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  fun fl -> 
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    (** Transform a (non-empty) list of formula to the conjunction
       made of those formula.  
    *)
    match fl with
	[] -> assert false
      | f::[] -> f
      | f1::f2::tail -> 
          List.fold_left (fun x y -> And(x, y)) (And(f1, f2)) tail

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let rec (formula_to_bdd : formula -> Bdd.t) =
  fun f ->
    (** Transform the formula [f] into a bdd. Also tabulates the
      result in the [bdd_tbl] field of [env_state] because the
      translation is very expensive.
    *)
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    try Hashtbl.find env_state.bdd_tbl f
    with Not_found -> 
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      let bdd =
	match f with 
	    Not(f) ->      Bdd.dnot (formula_to_bdd f)
	  | Or(f1, f2) ->  Bdd.dor (formula_to_bdd f1) (formula_to_bdd f2)
	  | And(f1, f2) -> Bdd.dand (formula_to_bdd f1) (formula_to_bdd f2)
	      
	  | True ->        Bdd.dtrue ()
	  | False ->       Bdd.dfalse ()
	  | Bvar(vn) ->    Bdd.var (Env_state.vn_to_index vn)
	      
	  | Eq(e1, e2) ->  assert false (* XXX FIX US !!! *)
	  | Ge(e1, e2) ->  assert false (* XXX FIX US !!! *)
	  | G(e1, e2)  ->  assert false (* XXX FIX US !!! *)
      in
      let _ = match f with 
	  Not(nf) -> Hashtbl.add env_state.bdd_tbl nf (Bdd.dnot bdd)
	| _  -> Hashtbl.add env_state.bdd_tbl (Not(f)) (Bdd.dnot bdd) 
      in
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(*      print_string ("$$$ building the bdd of " ^ (formula_to_string f) ^ "\n") ; *)
(*	flush stdout ; *)
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	Hashtbl.add env_state.bdd_tbl f bdd;
	bdd
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(****************************************************************************)

type var = int

(** In the following, we call a comb the bdd of a conjunction of
 litterals (var). They provide the ordering in which litterals
 appear in the bdds we manipulate.
*)


let rec (count_missing_vars: Bdd.t -> var -> int -> Bdd.t * int) =
  fun comb var cpt -> 
    (* Returns [cpt] + the number of variables occurring in [comb]
       before reaching [var] ([var] excluded). Also returns the comb
       which topvar is [var]. *)
    let _ = assert (not (Bdd.is_cst comb)) in
    let combvar = Bdd.topvar comb in
      if var = combvar
      then (comb, cpt)
      else count_missing_vars (Bdd.dthen comb) var (cpt+1)


let rec (build_sol_nb_table: Bdd.t -> Bdd.t -> sol_nb * sol_nb) =
  fun bdd comb -> 
    (** Returns the relative (to which bbd points to it) number of
      solutions of [bdd] and the one of its negation. Also udpates
      the solution number table [env_state.snt] for [bdd] and its
      negation, and recursively for all its sub-bdds. 
    *)
    let bdd_not = (Bdd.dnot bdd) in
    let (sol_nb, sol_nb_not) =
      try
	let (nt, ne) = Hashtbl.find env_state.snt bdd 
	and (not_nt, not_ne) = Hashtbl.find env_state.snt bdd_not in
	  (* solutions numbers in the table are absolute *)
	  ((add_sol_nb nt ne), (add_sol_nb not_nt not_ne))
      with Not_found ->  	
	let _ = assert (not (Bdd.is_cst bdd)) in
	let _ = assert ((Bdd.topvar bdd) = (Bdd.topvar comb)) in
	let (nt, not_nt) = compute_absolute_sol_nb (Bdd.dthen bdd) comb in
	let (ne, not_ne) = compute_absolute_sol_nb (Bdd.delse bdd) comb in

	let _ = assert (
(* 	  XXX Debugging stuff *)
	    let card_sol_t = (Bdd.cardinal (List.length (Bdd.int_of_support (Bdd.dthen comb))) (Bdd.dthen bdd)) in
	    let card_sol_e = (Bdd.cardinal (List.length (Bdd.int_of_support (Bdd.dthen comb))) (Bdd.delse bdd)) in
	    let nt_float = float_of_sol_nb nt in
	    let ne_float = float_of_sol_nb ne in
	      
	    let card_sol_t_not = (Bdd.cardinal (List.length (Bdd.int_of_support (Bdd.dthen comb))) (Bdd.dthen bdd_not)) in
	    let card_sol_e_not = (Bdd.cardinal (List.length (Bdd.int_of_support (Bdd.dthen comb))) (Bdd.delse bdd_not)) in
	    let nt_float_not = float_of_sol_nb not_nt in
	    let ne_float_not = float_of_sol_nb not_ne in
	      if
		(card_sol_t <> nt_float) || (card_sol_e <> ne_float) || 
		(card_sol_t_not <> nt_float_not) || (card_sol_e_not <> ne_float_not)  
	      then
		begin
		  print_string "Lurette computes: "; print_string (string_of_sol_nb (add_sol_nb nt ne));         
		  print_string " = ";print_string (string_of_sol_nb nt);         
		  print_string " + ";print_string (string_of_sol_nb ne);       
		  print_string "\nBdd.cardinal computes: ";   
		  print_float (Bdd.cardinal (List.length (Bdd.int_of_support comb)) bdd);       
		  print_string " = "; print_float card_sol_t;       
		  print_string " + "; print_float card_sol_e ;       
		  print_string "\n\n"; flush stdout ;
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		  Print.bdd_with_dot bdd (Env_state.index_to_vn) "bdd" ;
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		  print_string "(Not) Lurette computes: "; print_string (string_of_sol_nb (add_sol_nb not_nt not_ne));         
		  print_string " = ";print_string (string_of_sol_nb not_nt);         
		  print_string " + ";print_string (string_of_sol_nb not_ne);       
		  print_string "\nBdd.cardinal computes: ";   
		  print_float (Bdd.cardinal (List.length (Bdd.int_of_support comb)) bdd_not);       
		  print_string " = "; print_float card_sol_t_not;       
		  print_string " + "; print_float card_sol_e_not ;       
		  print_string "\n\n"; flush stdout ;
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		  Print.bdd_with_dot bdd_not (Env_state.index_to_vn) "bdd_not" ;
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		  Util.gv "bdd.ps"; 
		  Util.gv "bdd_not.ps"; 
		  false 
		end 
	      else
		true
	  )
	in
	  Hashtbl.add env_state.snt bdd (nt, ne) ;
	  Hashtbl.add env_state.snt bdd_not (not_nt, not_ne) ; 
	  ((add_sol_nb nt ne), (add_sol_nb not_nt not_ne))
    in
      (sol_nb, sol_nb_not)
and 
  (compute_absolute_sol_nb: Bdd.t -> Bdd.t -> sol_nb * sol_nb) =
  fun sub_bdd comb -> 
    (* returns the absolute number of solutions of [sub_bdd] (and its
       negation) w.r.t. [comb], where [comb] is the comb of the
       father of [sub_bdd]. *)
    if Bdd.is_cst sub_bdd 
    then 
      let sol_nb = (two_power_of (List.length (Bdd.int_of_support (Bdd.dthen comb)))) in
	if Bdd.is_true sub_bdd
	then (sol_nb, zero_sol) 
	else (zero_sol, sol_nb)
    else 
      let topvar = Bdd.topvar sub_bdd in
      let (sub_comb, missing_vars_nb) = 
	count_missing_vars (Bdd.dthen comb) topvar 0 
      in
      let (n0, not_n0) = build_sol_nb_table sub_bdd sub_comb in
      let factor = (two_power_of missing_vars_nb) in
	(mult_sol_nb n0 factor, mult_sol_nb not_n0 factor)
	
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(****************************************************************************)
(****************************************************************************)

let (toss_up_one_var: var -> var * bool) =
  fun var -> 
    let ran = Random.float 1. in
      if (ran < 0.5) then (var, true) else (var, false)
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let rec (draw_in_bdd: Bdd.t -> Bdd.t -> (var * bool) list) = 
  fun bdd comb ->
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    (** Returns a draw of the variables from the topvar of [bdd] to the end
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      (according to the ordering of the comb).
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    *)
    let _ = assert (not (Bdd.is_cst bdd)) in
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    let bddvar = Bdd.topvar bdd in
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    let combvar = Bdd.topvar comb in
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      if
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	bddvar = combvar
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      then
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	let _ = assert (Hashtbl.mem env_state.snt bdd) in
	let (n, m) = 
	  try Hashtbl.find env_state.snt bdd 
	  with Not_found -> 
(* 	    XXX Debugging stuff *)
(* 	    Print.bdd_with_dot bdd (Env_state.index_to_vn) ("bbd"^ "_" ^ (string_of_int (Hashtbl.hash bdd))) ; *)
(* 	    Print.snt env_state.snt;  *)
(* 	    print_int (Util.hashtbl_size env_state.snt);   *)
(* 	    flush stdout;  *)
	    assert false
	in
	let _ = assert (not ((eq_sol_nb n zero_sol) && (eq_sol_nb m zero_sol))) in
	let t = add_sol_nb n m in
  
	let _ = assert (
(* 	    XXX Debugging stuff *)
	  let card_sol_t = 
	    (Bdd.cardinal (List.length 
		(Bdd.int_of_support (Bdd.dthen comb))) (Bdd.dthen bdd))
	  and card_sol_e = 
	    (Bdd.cardinal (List.length 
		(Bdd.int_of_support (Bdd.dthen comb))) (Bdd.delse bdd))
	  and n_float = float_of_sol_nb n 
	  and m_float = float_of_sol_nb m 
	  in
	    if
	      ( (card_sol_t <> n_float) || (card_sol_e <> m_float) ) 
	      && (card_sol_t < 10. ** 12.) 
		(* Bdd.cardinal ougth to do rounding errors after 10^12 *)
	      && (card_sol_e < 10. ** 12.) 
	    then
	      begin
		print_string "Lurette computes: "; print_string (string_of_sol_nb t);         
		print_string " = ";print_string (string_of_sol_nb n);         
		print_string " + ";print_string (string_of_sol_nb m);       
		print_string "\nBdd.cardinal computes: ";   
		print_float (Bdd.cardinal (List.length (Bdd.int_of_support comb)) bdd);       
		print_string " = "; print_float card_sol_t;       
		print_string " + "; print_float card_sol_e ;       
		print_string "\n\n"; flush stdout ;
		Print.bdd_with_dot bdd (Env_state.index_to_vn) "bbd" ;
		Util.gv "bdd.ps";
		false
	    end 
	    else
	      true
	)
	in

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	let (bool, newbdd) =
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	  (* we draw [true] with the probability [n / (n + m)]. *)
	  if (eq_sol_nb m zero_sol) then (true, (Bdd.dthen bdd))
	  else if (eq_sol_nb n zero_sol) then (false, (Bdd.delse bdd))
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	  else 
	    let ran = Random.float 1. in
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	      if ran < ((float_of_sol_nb n) /. (float_of_sol_nb t))
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	      then (true, (Bdd.dthen bdd))
	      else (false, (Bdd.delse bdd))
	in
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	let _ = assert (not (Bdd.is_false newbdd)) 
		  (* a branch with no solution should not have been drawn ! *)
	in 
	  if Bdd.is_true newbdd then 
	    (bddvar, bool)::(List.map toss_up_one_var 
			       (Bdd.int_of_support (Bdd.dthen comb)))
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	  else
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	    (bddvar, bool)::(draw_in_bdd newbdd (Bdd.dthen comb))
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      else
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	(* Combvar <> topvar *)
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        (toss_up_one_var combvar)::(draw_in_bdd bdd (Bdd.dthen comb))

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(****************************************************************************)
(****************************************************************************)


(* Exported *)
let rec (is_satisfiable: formula list -> bool) = 
(* 
   As a side effect, also updates the [bdd_tbl] field of [env_state]
   with the bbd of [fl] (so that the expensive formula to bdd
   transcrition can be reused in [solve_formula]).
*)
  fun fl -> 
    let f = formula_list_to_conj fl in
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    let bdd = formula_to_bdd (formula_list_to_conj fl) in
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      not (Bdd.is_false bdd)
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(* Exported *)
let (solve_formula: int -> formula list -> var_name list -> (subst list * subst list) list) =
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  fun p fl vars_to_gen ->
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    let f = formula_list_to_conj fl in
    let bdd = Hashtbl.find env_state.bdd_tbl f in
    let vars_to_gen_f = 
      List.fold_left
	(fun acc vn -> (And(Bvar(vn), acc)))
	True
	vars_to_gen
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    in
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    let comb = formula_to_bdd vars_to_gen_f in
    let (draw_and_split : Bdd.t -> subst list * subst list) =
      fun bdd ->
	(* Draw values in the bdd *)
	let var_index_bool_l = draw_in_bdd bdd comb in
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        let subst_l = 
	  List.map 
	    (fun (i, b) -> 
	       (* Replace the indexes by the corresponding var names, 
		  and booleans by atomic_expr. *)
	       ((Env_state.index_to_vn i), Formula.Bool(b)))
	    var_index_bool_l 
	in 
	let _ = assert (
	  (* Checks that the generated variables are indeed the ones that should
	     have been generated... *)
	  let (gen_vars, _) = split subst_l in
            (sort (compare) gen_vars) = (sort (compare) vars_to_gen) )
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	in
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	let (out_vars, _) = List.split (env_state.output_var_names) in
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	  (* Splits output and local vars. *)
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          List.partition (fun (vn, _) -> List.mem vn out_vars) subst_l
    in
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(* XXX Recompute the solution number everytime as long as the bdds interface sucks *)
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    let _ =
      begin
	Hashtbl.clear env_state.snt ;
	Hashtbl.add env_state.snt
	  (Bdd.dtrue ()) (one_sol, zero_sol);
	Hashtbl.add env_state.snt
	  (Bdd.dfalse ()) (zero_sol, one_sol)
	end
    in
    let _ =
      if not (Hashtbl.mem env_state.snt bdd)
      then
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	let rec skip_var comb v =
	  if v = (Bdd.topvar comb) then comb else skip_var (Bdd.dthen comb) v
	in
	let comb2 = skip_var comb (Bdd.topvar bdd) in
	  build_sol_nb_table bdd comb2 
      else
	(zero_sol, zero_sol)
    in

      Util.unfold (draw_and_split) bdd p
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