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Alexandre Duret-Lutz
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36
buddy/examples/solitare/makefile
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36
buddy/examples/solitare/makefile
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# --------------------------------
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# Makefile for solitare test example
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# --------------------------------
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# --- Compiler flags
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CFLAGS = -O3 -pedantic -Wall -ansi -L../../src -I../../src
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# --- C++ compiler
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CPP = g++
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# --- C compiler
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CC = gcc
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# --- Do not touch ---
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.SUFFIXES: .cxx .c
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.cxx.o:
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$(CPP) $(CFLAGS) -c $<
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.c.o:
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$(CC) $(CFLAGS) -c $<
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solitare: solitare.o bddlib
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$(CPP) $(CFLAGS) solitare.o -o solitare -lbdd -lm
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bddlib:
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cd ../..; make
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clean:
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rm -f *~
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rm -f *.o
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rm -f solitare
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milner.o: ../../src/bdd.h
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35
buddy/examples/solitare/readme
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35
buddy/examples/solitare/readme
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SOLITARE GAME
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-------------
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This example tries to calculate the reachable state space of the
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Solitare game. The board is sketched below. At the beginning all
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places except number 17 has a pin in them. A pin may be moved by
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jumping over another pin into an empty place. The pin in between is
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then removed. The goal is to remove all pins execept one - which
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should be left in the center.
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It took a few hours to run this example on a Alpha machine and it
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required some 8000000 BDD nodes.
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(*****************************************************************************)
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(* *)
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(* ---------------- *)
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(* | 07 | 14 | 21 | *)
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(* ---------------- *)
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(* | 08 | 15 | 22 | *)
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(* ------------------------------------ *)
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(* | 01 | 04 | 09 | 16 | 23 | 28 | 31 | *)
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(* ------------------------------------ *)
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(* | 02 | 05 | 10 | 17 | 24 | 29 | 32 | *)
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(* ------------------------------------ *)
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(* | 03 | 06 | 11 | 18 | 25 | 30 | 33 | *)
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(* ------------------------------------ *)
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(* | 12 | 19 | 26 | *)
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(* ---------------- *)
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(* | 13 | 20 | 27 | *)
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(* ---------------- *)
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(* *)
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(*****************************************************************************)
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Thanks to Ken Larsen for his help with this example.
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222
buddy/examples/solitare/solitare.cxx
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222
buddy/examples/solitare/solitare.cxx
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#include <math.h>
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#include <time.h>
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#include <unistd.h>
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#include <stdlib.h>
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#include "bdd.h"
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float dummyStateNum; // Use to remove the number of states defined by the
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// next-state variables
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#define SIZE 33 // Size of the board
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#define CENTER 16 // Location of the center place
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bdd boardC[SIZE]; // Current state variables
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bdd boardN[SIZE]; // Next state variables
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bdd I; // Initial state
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bdd T; // Transition relation
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bdd currentvar; // All current state variables
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bddPair *pair; // Renaming pair
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// All the possible moves. Note that the numbering starts from '1'
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int moves[][3] =
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{ {1,4,9}, {1,2,3},
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{2,5,10},
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{3,2,1}, {3,6,11},
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{4,5,6}, {4,9,16},
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{5,10,17},
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{6,5,4}, {6,11,18},
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{7,8,9}, {7,14,21},
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{8,9,10}, {8,15,22},
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{9,8,7}, {9,10,11}, {9,4,1}, {9,16,23},
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{10,9,8}, {10,11,12}, {10,5,2}, {10,17,24},
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{11,10,9}, {11,12,13}, {11,6,3}, {11,18,25},
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{12,11,10}, {12,19,26},
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{13,12,11}, {13,20,27},
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{14,15,16},
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{15,16,17},
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{16,15,14}, {16,17,18}, {16,9,4}, {16,23,28},
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{17,16,15}, {17,18,19}, {17,10,5}, {17,24,29},
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{18,17,16}, {18,19,20}, {18,11,6}, {18,25,30},
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{19,18,17},
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{20,19,18},
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{21,22,23}, {21,14,7},
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{22,23,24}, {22,15,8},
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{23,22,21}, {23,24,25}, {23,16,9}, {23,28,31},
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{24,23,22}, {24,25,26}, {24,17,10}, {24,29,32},
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{25,24,23}, {25,26,27}, {25,18,11}, {25,30,33},
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{26,25,24}, {26,19,12},
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{27,26,25}, {27,20,13},
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{28,29,30}, {28,23,16},
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{29,24,17},
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{30,29,28}, {30,25,18},
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{31,32,33}, {31,28,23},
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{32,29,24},
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{33,32,31}, {33,30,25},
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{0,0,0}
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};
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// Setup the variables needed for the board
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void make_board(void)
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{
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bdd_setvarnum(SIZE*2);
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for (int n=0 ; n<SIZE ; n++)
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{
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boardC[n] = bdd_ithvar(n*2);
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boardN[n] = bdd_ithvar(n*2+1);
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}
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}
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// Make the initial state predicate
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void make_initial_state(void)
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{
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I = bddtrue;
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for (int n=0 ; n<SIZE ; n++)
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if (n == CENTER)
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I &= !boardC[n];
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else
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I &= boardC[n];
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}
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// Make sure all other places does nothing when
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// there's a move from 'src' to 'dst' over 'tmp'
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bdd all_other_idle(int src, int tmp, int dst)
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{
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bdd idle = bddtrue;
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for (int n=0 ; n<SIZE ; n++)
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{
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if (n != src && n != tmp && n != dst)
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idle &= bdd_biimp(boardC[n], boardN[n]);
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}
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return idle;
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}
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// Encode one move from 'src' to 'dst' over 'tmp'
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bdd make_move(int src, int tmp, int dst)
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{
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bdd move = boardC[src] & boardC[tmp] & !boardC[dst] &
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!boardN[src] & !boardN[tmp] & boardN[dst];
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move &= all_other_idle(src, tmp, dst);
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return move;
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}
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void make_transition_relation(void)
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{
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T = bddfalse;
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for (int n=0 ; moves[n][0]!=moves[n][1] ; n++)
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T |= make_move(moves[n][0]-1, moves[n][1]-1, moves[n][2]-1);
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cout << "Transition relation: " << bdd_nodecount(T) << " nodes, "
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<< bdd_satcount(T)/dummyStateNum << " states\n";
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}
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// Make renaming pair and current state variables
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void make_itedata(void)
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{
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pair = bdd_newpair();
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for (int n=0 ; n<SIZE ; n++)
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bdd_setpair(pair, n*2+1, n*2);
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currentvar = bddtrue;
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for (int n=0 ; n<SIZE ; n++)
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currentvar &= boardC[n];
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}
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// Do the forward iteration
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void iterate(void)
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{
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bdd tmp;
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bdd reachable = I;
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int cou = 1;
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make_itedata();
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do
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{
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tmp = reachable;
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bdd next = bdd_appex(reachable, T, bddop_and, currentvar);
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next = bdd_replace(next, pair);
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reachable |= next;
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cout << cou << ": " << bdd_nodecount(reachable)
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<< " nodes, " << bdd_satcount(reachable)/dummyStateNum
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<< " states\n" << flush;
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cou++;
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}
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while (tmp != reachable);
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}
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void iterate_front(void)
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{
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bdd tmp;
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bdd reachable = I;
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bdd front = reachable;
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int cou = 1;
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make_itedata();
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do
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{
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tmp = reachable;
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bdd next = bdd_appex(front, T, bddop_and, currentvar);
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next = bdd_replace(next, pair);
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front = next - reachable;
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reachable |= front;
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cout << cou << ": " << bdd_nodecount(reachable)
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<< " , " << bdd_satcount(reachable)/dummyStateNum << endl;
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cout << cou << ": " << bdd_nodecount(front)
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<< " , " << bdd_satcount(front)/dummyStateNum << endl;
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cou++;
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}
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while (tmp != reachable);
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}
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void setup(void)
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{
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bdd_init(100000,1000);
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bdd_setcacheratio(64);
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bdd_setmaxincrease(500000);
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dummyStateNum = pow(2.0, SIZE);
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make_board();
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make_transition_relation();
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make_initial_state();
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}
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int main(void)
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{
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long c1, c2;
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c1 = clock();
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setup();
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iterate();
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c2 = clock();
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printf("Time: %.1f sec.\n", ((float)(c2-c1))/CLOCKS_PER_SEC);
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system("ps aux | grep \"./solitare\" | grep -v \"grep\"");
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}
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