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76 lines
2.8 KiB
76 lines
2.8 KiB
// nand multiplex system
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// gxn/dxp 20/03/03
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// U (correctly) performs a random permutation of the outputs of the previous stage
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dtmc
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const int N; // number of inputs in each bundle
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const int K; // number of restorative stages
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const int M = 2*K+1; // total number of multiplexing units
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// parameters taken from the following paper
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// A system architecture solution for unreliable nanoelectric devices
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// J. Han & P. Jonker
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// IEEEE trans. on nanotechnology vol 1(4) 2002
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const double perr = 0.02; // probability nand works correctly
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const double prob1 = 0.9; // probability initial inputs are stimulated
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// model whole system as a single module by resuing variables
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// to decrease the state space
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module multiplex
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u : [1..M]; // number of stages
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c : [0..N]; // counter (number of copies of the nand done)
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s : [0..4]; // local state
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// 0 - initial state
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// 1 - set x inputs
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// 2 - set y inputs
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// 3 - set outputs
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// 4 - done
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z : [0..N]; // number of new outputs equal to 1
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zx : [0..N]; // number of old outputs equal to 1
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zy : [0..N]; // need second copy for y
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// initially 9 since initially probability of stimulated state is 0.9
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x : [0..1]; // value of first input
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y : [0..1]; // value of second input
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[] s=0 & (c<N) -> (s'=1); // do next nand if have not done N yet
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[] s=0 & (c=N) & (u<M) -> (s'=1) & (zx'=z) & (zy'=z) & (z'=0) & (u'=u+1) & (c'=0); // move on to next u if not finished
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[] s=0 & (c=N) & (u=M) -> (s'=4) & (zx'=0) & (zy'=0) & (x'=0) & (y'=0); // finished (so reset variables not needed to reduce state space)
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// choose x permute selection (have zx stimulated inputs)
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// note only need y to be random
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[] s=1 & u=1 -> prob1 : (x'=1) & (s'=2) + (1-prob1) : (x'=0) & (s'=2); // initially random
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[] s=1 & u>1 & zx>0 -> (x'=1) & (s'=2) & (zx'=zx-1);
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[] s=1 & u>1 & zx=0 -> (x'=0) & (s'=2);
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// choose x randomly from selection (have zy stimulated inputs)
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[] s=2 & u=1 -> prob1 : (y'=1) & (s'=3) + (1-prob1) : (y'=0) & (s'=3); // initially random
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[] s=2 & u>1 & zy<(N-c) & zy>0 -> zy/(N-c) : (y'=1) & (s'=3) & (zy'=zy-1) + 1-(zy/(N-c)) : (y'=0) & (s'=3);
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[] s=2 & u>1 & zy=(N-c) & c<N -> 1 : (y'=1) & (s'=3) & (zy'=zy-1);
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[] s=2 & u>1 & zy=0 -> 1 : (y'=0) & (s'=3);
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// use nand gate
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[] s=3 & z<N & c<N -> (1-perr) : (z'=z+(1-x*y)) & (s'=0) & (c'=c+1) & (x'=0) & (y'=0) // not faulty
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+ perr : (z'=z+(x*y)) & (s'=0) & (c'=c+1) & (x'=0) & (y'=0); // von neumann fault
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// [] s=3 & z<N -> (1-perr) : (z'=z+(1-x*y)) & (s'=0) & (c'=c+1) & (x'=0) & (y'=0) // not faulty
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// + perr : (z'=z+(x*y)) & (s'=0) & (c'=c+1) & (x'=0) & (y'=0); // von neumann fault
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[] s=4 -> (s'=s);
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endmodule
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// rewards: final value of gate
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rewards
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// [] s=0 & (c=N) & (u=M) : z/N;
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s=0 & (c=N) & (u=M) : z/N;
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endrewards
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label "target" = s=4 & z/N<0.1;
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label "end" = s=4;
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