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