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Detecting State Coding Conflicts in STGs Using SAT

Detecting State Coding Conflicts in STGs Using SAT. Victor Khomenko , Maciej Koutny , and Alex Yakovlev University of Newcastle upon Tyne. Talk Outline. Introduction Asynchronous circuits Complete state coding (CSC) State graphs vs. net unfoldings

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Detecting State Coding Conflicts in STGs Using SAT

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  1. Detecting State CodingConflicts in STGs Using SAT Victor Khomenko, Maciej Koutny, and Alex Yakovlev University of Newcastle upon Tyne

  2. Talk Outline • Introduction • Asynchronous circuits • Complete state coding (CSC) • State graphs vs. net unfoldings • Translating a CSC problem into a SAT one • Analysis of the method • Experimental results • Future work

  3. Asynchronous Circuits Asynchronous circuits – no clocks: • Low power consumption • Average-case rather than worst-case performance • Low electro-magnetic emission • No problems with the clock skew • Hard to synthesize • The theory is not sufficiently developed • Limited tool support

  4. Data Transceiver Device Bus d lds dsr VME Bus Controller dsw ldtack dtack dtack- dsr+ lds+ d- lds- ldtack- ldtack+ dsr- dtack+ d+ Example: VME Bus Controller

  5. 10000 dtack- dsr+ 01000 00000 lds+ ldtack- ldtack- ldtack- dtack- dsr+ 10100 01010 00010 10010 ldtack+ lds- lds- lds- dtack- dsr+ 10110 01110 10110 M’’ M’ 00110 d+ d- dsr- dtack+ 01111 11111 10111 Example: CSC Conflict

  6. M’’ M’ Example: enforcing CSC dtack- dsr+ csc+ 010000 100000 000000 100001 lds+ ldtack- ldtack- ldtack- dtack- dsr+ 010100 101001 000100 100100 ldtack+ lds- lds- lds- dtack- dsr+ 101101 011100 101100 001100 d+ d- dsr- dtack+ csc- 011111 111111 101111 011110

  7. State Graphs vs. Unfoldings State Graphs: • Relatively easy theory • Many efficient algorithms • Not visual • State space explosion problem

  8. State Graphs vs. Unfoldings Unfoldings: • Alleviate the state space explosion problem • More visual than state graphs • Proven efficient for model checking • Quite complicated theory • Not sufficiently investigated • Relatively few algorithms

  9. e8 e10 dtack- dsr+ e1 e2 e3 e4 e5 e6 e7 e12 lds+ dsr+ lds+ ldtack+ dtack+ d+ dsr- d- e9 e11 lds- ldtack- Translation Into a SAT Problem • Configuration constraint: conf’ and conf’’ are configurations • Encoding constraint: Code(conf’) = Code(conf’’) • Separating constraint: Out(conf’)  Out(conf’’) conf’’=111111110100 conf’=111000000000 Code(conf’’)=10110 Code(conf’)=10110

  10. Translation Into a SAT Problem Conf(conf ')  Conf(conf '')  Code(conf ',…, val)  Code(conf '',…, val)  Out(conf ',…, out')  Out(conf '',…, out'')  out' out''

  11. Configuration constraint Conf(conf ')  Conf(conf '') Code(conf ',…, val)  Code(conf '',…, val)  Out(conf ',…, out')  Out(conf '',…, out'')  out' out''

  12. 1 1 1 e 1 causality 0 1 e 0 no conflicts Configuration constraint

  13. ldtack- lds+ lds- ldtack+ dtack+ dsr+ lds+ dsr- d+ d- dsr+ dtack- dsw+ lds+ d+ ldtack+ dtack+ dtack+ dsw+ dsw- lds+ d+ d- The efficiency of the BCP rule 1

  14. ldtack- lds+ lds- ldtack+ dtack+ dsr+ lds+ dsr- d+ d- dsr+ dtack- dsw+ lds+ d+ ldtack+ dtack+ dtack+ dsw+ dsw- lds+ d+ d- The efficiency of the BCP rule 0

  15. Encoding constraint Conf(conf ')  Conf(conf '')  Code(conf ',…, val)  Code(conf '',…, val)  Out(conf ',…, out')  Out(conf '',…, out'')  out' out''

  16. a+ b+ c+ a- c- a+ a=0 a=1 Tracing the value of a signal

  17. 0 0 1 e b 0 Computing the signals’ values

  18. Separating constraint Conf(conf ')  Conf(conf '')  Code(conf ',…, val)  Code(conf '',…, val)  Out(conf ',…, out')  Out(conf '',…, out'')  out' out''

  19. 1 0 1 0 e 1 0 Computing the enabled outputs

  20. Translation Into a SAT Problem Conf(conf ')  Conf(conf '')  Code(conf ',…, val)  Code(conf '',…, val)  Out(conf ',…, out')  Out(conf '',…, out'')  out' out''

  21. Analysis of the Method • A lot of clauses of length 2 – good for BCP • The method can be generalized to other coding properties, e.g. USC and normalcy • The method can be generalized to nets with dummy transitions • Further optimization is possible for certain net subclasses, e.g. unique-choice nets

  22. Experimental Results • Unfoldings of STGs are almost always small in practice and thus well-suited for synthesis • Huge memory savings • Dramatic speedups: • A few intractable examples easily solved • Several orders of magnitude speedups for many other examples • The hardest example we tested took less than 3 minutes

  23. A philosophical remark The combination unfolding & solver seems to be quite powerful: unfolding reduces a PSPACE-complete problem down to an NP-complete one, which can efficiently be tackled by a solver

  24. Future Work What about a full design cycle based on PN unfoldings?

  25. Thank you! Any questions?

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