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51 lines
1.7 KiB
51 lines
1.7 KiB
// randomized dining philosophers [LR81]
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// dxp/gxn 23/01/02
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// model which does not require fairness
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// remove the possibility of loops:
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// (1) cannot stay in thinking
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// (2) if first fork not free then cannot move (another philosopher must more)
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mdp
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// atomic formulae
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// left fork free and right fork free resp.
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formula lfree = p2=0..4,6,10;
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formula rfree = p7=0..3,5,7,11;
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module phil1
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p1: [0..11];
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[] p1=0 -> (p1'=1); // trying
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[] p1=1 -> 0.5 : (p1'=2) + 0.5 : (p1'=3); // draw randomly
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[] p1=2 & lfree -> (p1'=4); // pick up left
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[] p1=3 & rfree -> (p1'=5); // pick up right
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[] p1=4 & rfree -> (p1'=8); // pick up right (got left)
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[] p1=4 & !rfree -> (p1'=6); // right not free (got left)
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[] p1=5 & lfree -> (p1'=8); // pick up left (got right)
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[] p1=5 & !lfree -> (p1'=7); // left not free (got right)
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[] p1=6 -> (p1'=1); // put down left
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[] p1=7 -> (p1'=1); // put down right
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[] p1=8 -> (p1'=9); // move to eating (got forks)
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[] p1=9 -> (p1'=10); // finished eating and put down left
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[] p1=9 -> (p1'=11); // finished eating and put down right
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[] p1=10 -> (p1'=0); // put down right and return to think
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[] p1=11 -> (p1'=0); // put down left and return to think
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endmodule
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// construct further modules through renaming
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module phil2 = phil1 [p1=p2, p2=p3, p7=p1] endmodule
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module phil3 = phil1 [p1=p3, p2=p4, p7=p2] endmodule
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module phil4 = phil1 [p1=p4, p2=p5, p7=p3] endmodule
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module phil5 = phil1 [p1=p5, p2=p6, p7=p4] endmodule
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module phil6 = phil1 [p1=p6, p2=p7, p7=p5] endmodule
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module phil7 = phil1 [p1=p7, p2=p1, p7=p6] endmodule
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// rewards (number of steps)
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rewards
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[] true : 1;
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endrewards
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