Detecting State Coding Conflicts in STGs Using Integer Programming

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Detecting State Coding Conflicts in STGs Using
Integer Programming

• Victor Khomenko, Maciej Koutny, and Alex Yakovlev
• University of Newcastle upon Tyne

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Talk Outline

• Introduction
• Asynchronous circuits (AC)
• Algorithmic problems in AC synthesis
• State graphs vs. net unfoldings
• Translating a CSC problem into an IP problem
• Solving the IP problem
• Analysis of the algorithm
• Experimental results
• Future work

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Asynchronous Circuits

• AC circuits without 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

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Example VME Bus Controller
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Problems in AC Synthesis

• Checking consistency
• Checking semi-modularity
• Deadlock detection
• Checking CSC
• Enforcing CSC
• Deriving equations
• Technology mapping

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Example CSC Conflict
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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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State Graphs vs. Unfoldings

• SG Unf
• Checking consistency ? ?
• Checking semi-modularity ? ?
• Deadlock detection ? ?
• Checking CSC ? ?
• Enforcing CSC ? ?
• Deriving equations ? ?
• Technology mapping ? ?

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Translation Into an IP Problem
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Translation Into an IP Problem
Code(x)Code(x)
M0 I x ? 0 M0 I x ? 0
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Solving the IP Problem
1
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Solving the IP Problem
0
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Solving the IP Problem
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Analysis of the Algorithm

• Moderate memory requirements O(E)
• The algorithm can be stopped after the first
  solution is found
• Usual IP solvers heuristics can be applied
• The algorithm can easily be generalized to check
  other coding properties, e.g. USC and normalcy
• Optimization is possible for certain net
  subclasses, e.g. unique-choice nets

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Experimental Results

• Unfoldings are usually not much bigger than the
  original STGs, i.e. unfoldings are well-suited
  for synthesis
• If there is a CSC conflict the algorithm finds it
  almost instantly
• If there is no CSC conflict the algorithm proves
  this in a reasonable time, often faster than
  BDD-based algorithms
• No page swapping!

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Future Work

• SG Unf
• Checking consistency ? ?
• Checking semi-modularity ? ?
• Deadlock detection ? ?
• Checking CSC ? ?
• Enforcing CSC ? ?
• Deriving equations ? ?
• Technology mapping ? ?