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72 lines
2.4 KiB
72 lines
2.4 KiB
// twelve 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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nondeterministic
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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..8];
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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..8];
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r1 : [0..2];
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// enter trying
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[] p1=0 -> (p1'=0);
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// remain in remainder
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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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+ 0.0078125 : (b1'=7) & (r1'=r) & (b'=max(b,7))
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+ 0.0078125 : (b1'=8) & (r1'=r) & (b'=max(b,8));
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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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module process9 = process1 [p1=p9, b1=b9, r1=r9] endmodule
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module process10 = process1 [p1=p10, b1=b10, r1=r10] endmodule
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module process11 = process1 [p1=p11, b1=b11, r1=r11] endmodule
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module process12 = process1 [p1=p12, b1=b12, r1=r12] endmodule
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