From: acondolu <andrea.condoluci@unibo.it>
Date: Sat, 15 Jul 2017 13:31:50 +0000 (+0200)
Subject: Encoding of SAT problems and 3-colorability of graphs
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=48099a8d17ed96681087fa7e7c507dc2ec209125;p=fireball-separation.git

Encoding of SAT problems and 3-colorability of graphs
---

diff --git a/ocaml/Makefile b/ocaml/Makefile
index 430f159..0f00f14 100644
--- a/ocaml/Makefile
+++ b/ocaml/Makefile
@@ -13,6 +13,9 @@ a.out: $(UTILS) lambda4.cmx problems.cmx
 
 # test.out: $(UTILS) lambda3.cmx test1.ml
 # 	$(OCAMLC) -o test.out $(LIB) $^
+
+sat.out: $(UTILS) lambda4.cmx sat.ml
+	$(OCAMLC) -o sat.out $(LIB) $^
 #
 test4.out: $(UTILS) lambda4.cmx test.ml
 	$(OCAMLC) -o test4.out $(LIB) $^
diff --git a/ocaml/sat.ml b/ocaml/sat.ml
new file mode 100644
index 0000000..ceb90ca
--- /dev/null
+++ b/ocaml/sat.ml
@@ -0,0 +1,131 @@
+(*
+ Reductions from SAT and 3-colorability of graphs to separation
+ of lambda-terms. Commented out the encoding from SAT.
+*)
+
+(* type cnf = int list list;;
+
+let (++) f g x = f (g x);;
+
+let maxvar : cnf -> int =
+ let aux f = List.fold_left (fun acc x -> max acc (f x)) 0 in
+ aux (aux abs)
+;; *)
+
+type graph = (int * int) list;;
+
+let arc x y = min x y, max x y;;
+let mem g x y = List.mem (arc x y) g;;
+
+(* let reduction_sat_3col p =
+ let triangle a0 a1 a2 = [arc a0 a1; arc a0 a2; arc a1 a2] in
+ let init0 = triangle 0 1 2 in
+ (* 0false; 1true; 2base*)
+ let n = maxvar p in
+ let init1 = Array.to_list (Array.mapi (fun i () -> triangle (2*i+1) (2*(i+1)) 2) (Array.make n ())) in
+ let freshno = ref (2 * n + 3) in
+ let mk_triangle () =
+  let i = !freshno in
+  freshno := i+3; i, i+1, i+2 in
+ let rec translate = function
+ | [] -> assert false
+ | x::[] -> [triangle 0 2 x]
+ | x::y::l ->
+    let a,b,c = mk_triangle () in
+    triangle a b c :: [arc x a; arc y b] :: translate (c::l) in
+ let p = List.map (List.map (fun x ->
+   if x = 0 then assert false
+    else if x < 0 then 2 * (abs x + 1)
+    else 2 * x + 1
+  )) p in
+ let init2 = List.map (List.concat ++ translate) p in
+ !freshno, init0 @ List.concat (init1 @ init2)
+;;
+
+let string_of_graph g =
+ String.concat " " (List.map (fun (x,y) -> string_of_int x ^ "<>" ^ string_of_int y) g)
+;; *)
+
+(* let main p =
+ let mv = maxvar p in
+ prerr_endline (string_of_int mv);
+ let _, g = reduction_sat_3col p in
+ prerr_endline (string_of_graph g);
+ generate ;;
+
+prerr_endline (main[
+ [1; -2; 3];
+ [2; 4; -5]
+]);; *)
+
+let p_ = "BOMB ";;
+let x_ = "x ";;
+(* y, z dummies *)
+let y_ = "y ";;
+let z_ = "z ";;
+(* a, b endline separators *)
+let a_ = "a ";;
+let b_ = "b ";;
+
+let generate g n max =
+ (* 0 <= n <= max+1 *)
+ let three f sep =
+  String.concat sep (List.map f [0;1;2]) in
+ let rec aux' n m color =
+  if m = -1 then x_
+  else aux' n (m-1) color ^
+   if n = m then
+     (if List.mem (n,n) g then p_^p_^p_ (* cappio nel grafo *)
+      else three (fun c -> if color = c then y_ else p_) "")
+   else if n < m then y_^y_^y_
+   else if List.mem (m,n) g then
+    three (fun c -> if color = c then p_ else y_) ""
+   else y_^y_^y_ in
+ let rec aux m =
+  if m = -1 then x_
+   else aux (m-1) ^
+    if n < m then p_^p_^p_
+    else if n = m then
+      "(_." ^ three (aux' n max) "b) (_." ^ "b) "
+    else y_^y_^y_
+ in aux max ^ a_
+;;
+
+let generate2 g n max =
+ let rec aux m =
+  if m = -1 then x_
+   else aux (m-1) ^
+    if n < m then p_^p_^p_
+    else if n = m
+    then z_^z_^z_
+    else y_^y_^y_
+ in aux max ^ p_
+;;
+
+
+let encode_graph g =
+ let g = List.map (fun (x,y) -> min x y, max x y) g in
+ let mapi f a = Array.to_list (Array.mapi f a) in
+ let nodex_no =
+  List.fold_left (fun acc (a,b) -> Pervasives.max acc (Pervasives.max a b)) 0 in
+ String.concat "\n" ("\n$ problem from 3-colorability" ::
+  let no = nodex_no g in
+  mapi (fun i () ->
+    (if i = no+1 then "D " else "C ") ^ generate g i no
+  ) (Array.make (no+2) ()) @
+  mapi (fun i () ->
+    "C " ^ generate2 g i no
+  ) (Array.make (no+1) ());
+ )
+;;
+
+(* easy one *)
+prerr_endline (encode_graph [0,1;]);;
+
+(* two imopssible problems *)
+prerr_endline (
+ encode_graph [0,1; 1,1]
+);;
+prerr_endline (
+ encode_graph [0,1; 0,2; 1,2; 0,3; 1,3; 2,3]
+);;
diff --git a/ocaml/sat.mli b/ocaml/sat.mli
new file mode 100644
index 0000000..77f0239
--- /dev/null
+++ b/ocaml/sat.mli
@@ -0,0 +1,3 @@
+type graph = (int * int) list
+
+val encode_graph : graph -> string