Detecting State Coding Conflicts in STGs Using SAT

1
Detecting State Coding Conflicts 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
Example VME Bus Controller
5
Example CSC Conflict
6
Example enforcing CSC
dtack-
dsr
csc
010000
000000
100000
100001
lds
ldtack-
ldtack-
ldtack-
dtack-
dsr
010100
101001
000100
100100
ldtack
lds-
lds-
lds-
dtack-
dsr
101101
011100
101100
001100
d
d-
dtack
dsr-
csc-
011111
111111
101111
011110
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State Graphs vs. Unfoldings

• State Graphs
• Relatively easy theory
• Many efficient algorithms
• Not visual
• State space explosion problem

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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

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Translation Into a SAT Problem
conf111111110100
conf111000000000
Code(conf)10110
Code(conf)10110

• Configuration constraint conf and conf are
  configurations
• Encoding constraint Code(conf) Code(conf)
• Separating constraint Out(conf) ? Out(conf)

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Translation Into a SAT Problem
Conf(conf ') ? Conf(conf '') ? Code(conf
',, val) ? Code(conf '',, val) ? Out(conf
',, out') ? Out(conf '',, out'') ? out'?
out''
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Configuration constraint
Conf(conf ') ? Conf(conf '') ? Code(conf
',, val) ? Code(conf '',, val) ? Out(conf
',, out') ? Out(conf '',, out'') ? out'?
out''
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Configuration constraint
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The efficiency of the BCP rule
1
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The efficiency of the BCP rule
0
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Encoding constraint
Conf(conf ') ? Conf(conf '') ? Code(conf
',, val) ? Code(conf '',, val) ? Out(conf
',, out') ? Out(conf '',, out'') ? out'?
out''
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Tracing the value of a signal
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Computing the signals values
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Separating constraint
Conf(conf ') ? Conf(conf '') ? Code(conf
',, val) ? Code(conf '',, val) ? Out(conf
',, out') ? Out(conf '',, out'') ? out'?
out''
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Computing the enabled outputs
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Translation Into a SAT Problem
Conf(conf ') ? Conf(conf '') ? Code(conf
',, val) ? Code(conf '',, val) ? Out(conf
',, out') ? Out(conf '',, out'') ? out'?
out''
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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?