151 lines
4.1 KiB
Plaintext
151 lines
4.1 KiB
Plaintext
/*
|
|
Article: 5653 of comp.lang.prolog
|
|
Newsgroups: comp.lang.prolog
|
|
Path: ecrc!Germany.EU.net!mcsun!ub4b!news.cs.kuleuven.ac.be!bimbart
|
|
From: bimbart@cs.kuleuven.ac.be (Bart Demoen)
|
|
Subject: boolean constraint solvers
|
|
Message-ID: <1992Oct19.093131.11399@cs.kuleuven.ac.be>
|
|
Sender: news@cs.kuleuven.ac.be
|
|
Nntp-Posting-Host: hera.cs.kuleuven.ac.be
|
|
Organization: Dept. Computerwetenschappen K.U.Leuven
|
|
Date: Mon, 19 Oct 1992 09:31:31 GMT
|
|
Lines: 120
|
|
|
|
?- calc_constr(N,C,L) . % with N instantiated to a positive integer
|
|
|
|
generates in the variable C a datastructure that can be interpreted as a
|
|
boolean expression (and in fact is so by SICStus Prolog's bool:sat) and in L
|
|
the list of variables involved in this boolean expression; so
|
|
|
|
?- calc_constr(N,C,L) , bool:sat(C) , bool:labeling(L) .
|
|
% with N instantiated to a positive integer
|
|
|
|
shows the instantiations of L for which the boolean expression is true
|
|
e.g.
|
|
|
|
| ?- calc_constr(3,C,L) , bool:sat(C) , bool:labeling(L) .
|
|
% C = omitted
|
|
L = [1,0,1,0,1,0,1,0,1] ? ;
|
|
|
|
no
|
|
|
|
it is related to a puzzle which I can describe if people are interested
|
|
|
|
SICStus Prolog can solve this puzzle up to N = 9 on my machine; it then
|
|
fails because of lack of memory (my machine has relatively little: for N=9
|
|
SICStus needs 14 Mb - and about 50 secs runtime + 20 secs for gc on Sparc 1)
|
|
|
|
I am interested in hearing about boolean constraint solvers that can deal with
|
|
the expression generated by the program below, for large N and in reasonable
|
|
time and space; say N in the range 10 to 20: the number of solutions for
|
|
different N varies wildly; there is exactly one solution for N = 10,12,13,15,20
|
|
but for N=18 or 19 there are several thousand, so perhaps it is best to
|
|
restrict attention to N with only one solution - unless that is unfair to your
|
|
solver
|
|
|
|
in case you have to adapt the expression for your own boolean solver, in
|
|
the expression generated, ~ means negation, + means disjunction,
|
|
* means conjunction and somewhere in the program, 1 means true
|
|
|
|
|
|
Thanks
|
|
|
|
Bart Demoen
|
|
*/
|
|
|
|
|
|
% test(N,L) :- calc_constr(N,C,L) , bool:sat(C) , bool:labeling(L) .
|
|
test(N,L) :- calc_constr(N,C,L) , solve_bool(C,1).
|
|
testbl(N,L) :- calc_constr(N,C,L) , solve_bool(C,1), labeling.
|
|
testul(N,L) :- calc_constr(N,C,L) , solve_bool(C,1), label_bool(L).
|
|
|
|
calc_constr(N,C,L) :-
|
|
M is N * N ,
|
|
functor(B,b,M) ,
|
|
B =.. [_|L] ,
|
|
cc(N,N,N,B,C,1) .
|
|
|
|
cc(0,M,N,B,C,T) :- ! ,
|
|
NewM is M - 1 ,
|
|
cc(N,NewM,N,B,C,T) .
|
|
cc(_,0,_,B,C,C) :- ! .
|
|
cc(I,J,N,B,C,T) :-
|
|
neighbours(I,J,N,B,C,S) ,
|
|
NewI is I - 1 ,
|
|
cc(NewI,J,N,B,S,T) .
|
|
|
|
|
|
neighbours(I,J,N,B,C,S) :-
|
|
add(I,J,N,B,L,R1) ,
|
|
add(I-1,J,N,B,R1,R2) ,
|
|
add(I+1,J,N,B,R2,R3) ,
|
|
add(I,J-1,N,B,R3,R4) ,
|
|
add(I,J+1,N,B,R4,[]) , % L is the list of neighbours of (I,J)
|
|
% including (I,J)
|
|
odd(L,C,S) .
|
|
|
|
add(I,J,N,B,S,S) :- I =:= 0 , ! .
|
|
add(I,J,N,B,S,S) :- J =:= 0 , ! .
|
|
add(I,J,N,B,S,S) :- I > N , ! .
|
|
add(I,J,N,B,S,S) :- J > N , ! .
|
|
add(I,J,N,B,[X|S],S) :- A is (I-1) * N + J , arg(A,B,X) .
|
|
|
|
|
|
% odd/2 generates the constraint that an odd number of elements of its first
|
|
% argument must be 1, the rest must be 0
|
|
|
|
odd(L,C*S,S):- exors(L,C).
|
|
|
|
exors([X],X).
|
|
exors([X|L],X#R):- L=[_|_],
|
|
exors(L,R).
|
|
|
|
|
|
/*
|
|
% did this by enumeration, because there are only 4 possibilities
|
|
|
|
odd([A], A * S,S) :- ! .
|
|
|
|
odd([A,B,C], ((A * ~~(B) * ~~(C)) +
|
|
(A * B * C) +
|
|
( ~~(A) * B * ~~(C)) +
|
|
( ~~(A) * ~~(B) * C)) * S,S)
|
|
:- ! .
|
|
|
|
odd([A,B,C,D], ((A * ~~(B) * ~~(C) * ~~(D)) +
|
|
(A * B * C * ~~(D)) +
|
|
(A * B * ~~(C) * D) +
|
|
(A * ~~(B) * C * D) +
|
|
( ~~(A) * B * ~~(C) * ~~(D)) +
|
|
( ~~(A) * B * C * D) +
|
|
( ~~(A) * ~~(B) * C * ~~(D)) +
|
|
( ~~(A) * ~~(B) * ~~(C) * D)) * S,S )
|
|
:- ! .
|
|
|
|
odd([A,B,C,D,E],((A * ~~(B) * ~~(C) * ~~(D) * ~~(E)) +
|
|
(A * B * C * ~~(D) * ~~(E)) +
|
|
(A * B * ~~(C) * D * ~~(E)) +
|
|
(A * ~~(B) * C * D * ~~(E)) +
|
|
(A * B * ~~(C) * ~~(D) * E) +
|
|
(A * ~~(B) * C * ~~(D) * E) +
|
|
(A * ~~(B) * ~~(C) * D * E) +
|
|
(A * B * C * D * E) +
|
|
( ~~(A) * B * ~~(C) * ~~(D) * ~~(E)) +
|
|
( ~~(A) * B * ~~(C) * D * E) +
|
|
( ~~(A) * B * C * ~~(D) * E) +
|
|
( ~~(A) * B * C * D * ~~(E)) +
|
|
( ~~(A) * ~~(B) * C * ~~(D) * ~~(E)) +
|
|
( ~~(A) * ~~(B) * C * D * E) +
|
|
( ~~(A) * ~~(B) * ~~(C) * D * ~~(E)) +
|
|
( ~~(A) * ~~(B) * ~~(C) * ~~(D) * E)) * S,S ) :- ! .
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|