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79 lines
2.5 KiB
79 lines
2.5 KiB
// N-processor mutual exclusion [Rab82]
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// with global variables to remove sychronization
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// gxn/dxp 02/02/00
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mdp
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// size of shared counter
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const int K = 7; // 4+ceil(log_2 N)
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// global variables (all modules can read and write)
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// c=0 critical section free
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// c=1 critical section not free
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// b current highest draw
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// r current round
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global c : [0..1];
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global b : [0..K];
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global r : [1..2];
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// local variables: process i
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// state: pi
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// 0 remainder
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// 1 trying
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// 2 critical section
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// current draw: bi
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// current round: ri
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// atomic formula for process 1 drawing
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formula draw = p1=1 & (b<b1 | r!=r1);
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module process1
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p1 : [0..2];
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b1 : [0..K];
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r1 : [0..2];
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// remain in remainder
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[] p1=0 -> (p1'=0);
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// enter trying
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[] p1=0 -> (p1'=1);
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// make a draw
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[] draw -> 0.5 : (b1'=1) & (r1'=r) & (b'=max(b,1))
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+ 0.25 : (b1'=2) & (r1'=r) & (b'=max(b,2))
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+ 0.125 : (b1'=3) & (r1'=r) & (b'=max(b,3))
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+ 0.0625 : (b1'=4) & (r1'=r) & (b'=max(b,4))
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+ 0.03125 : (b1'=5) & (r1'=r) & (b'=max(b,5))
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+ 0.015625 : (b1'=6) & (r1'=r) & (b'=max(b,6))
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+ 0.015625 : (b1'=7) & (r1'=r) & (b'=max(b,7));
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// enter critical section and randomly set r to 1 or 2
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[] p1=1 & b=b1 & r=r1 & c=0 -> 0.5 : (r'=1) & (c'=1) & (b'=0) & (b1'=0) & (r1'=0) & (p1'=2)
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+ 0.5 : (r'=2) & (c'=1) & (b'=0) & (b1'=0) & (r1'=0) & (p1'=2);
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// loop when trying and cannot make a draw or enter critical section
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[] p1=1 & r1=r & b1<=b & ((c=0 & b1!=b) | c=1) -> (p1'=p1);
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// leave crictical section
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[] p1=2 -> (p1'=0) & (c'=0);
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// stay in critical section
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[] p1=2 -> (p1'=2);
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endmodule
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// construct further modules through renaming
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module process2 = process1 [p1=p2, b1=b2, r1=r2] endmodule
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module process3 = process1 [p1=p3, b1=b3, r1=r3] endmodule
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module process4 = process1 [p1=p4, b1=b4, r1=r4] endmodule
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module process5 = process1 [p1=p5, b1=b5, r1=r5] endmodule
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module process6 = process1 [p1=p6, b1=b6, r1=r6] endmodule
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module process7 = process1 [p1=p7, b1=b7, r1=r7] endmodule
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module process8 = process1 [p1=p8, b1=b8, r1=r8] endmodule
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// formulas/labels for use in properties:
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// number of processes in critical section
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formula num_procs_in_crit = (p1=2?1:0)+(p2=2?1:0)+(p3=2?1:0)+(p4=2?1:0)+(p5=2?1:0)+(p6=2?1:0)+(p7=2?1:0)+(p8=2?1:0);
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// one of the processes is trying
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label "one_trying" = p1=1|p2=1|p3=1|p4=1|p5=1|p6=1|p7=1|p8=1;
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// one of the processes is in the critical section
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label "one_critical" = p1=2|p2=2|p3=2|p4=2|p5=2|p6=2|p7=2|p8=2;
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