A sat based fitness function for evolutionary optimization of polymorphic circuits
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A SAT-based Fitness Function for Evolutionary Optimization of Polymorphic Circuits. Lukas Sekanina and Zdenek Vasicek. DATE’12. OUTLINE. 1. INTRODUCTION 2. POLYMORPHIC CIRCUITS 3. DIRECT EVOLUTION OF POLYMORPHIC CIRCUITS USING CGP

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A SAT-based Fitness Function for Evolutionary Optimization of Polymorphic Circuits

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A sat based fitness function for evolutionary optimization of polymorphic circuits

A SAT-based Fitness Function for EvolutionaryOptimization of Polymorphic Circuits

Lukas Sekanina and ZdenekVasicek

DATE’12


Outline

OUTLINE

  • 1.INTRODUCTION

  • 2. POLYMORPHIC CIRCUITS

  • 3. DIRECT EVOLUTION OF POLYMORPHIC CIRCUITS USING CGP

  • 4. PROPOSED FITNESS EVALUATION FOR POLYMORPHIC CIRCUITS

  • 5.RESULTS

  • 6. CONCLUSIONS


Introduction

INTRODUCTION

  • Polymorphic gates were described by the NASA JPL evolvable hardware group in2001 [1]

  • Graphene reconfigurable logic devices, discovered at IBM T. J. Watson ResearchCenter, were presented in 2010[2].


Introduction1

INTRODUCTION


Polymorphic circuits

POLYMORPHIC CIRCUITS

  • A.Polymorphic Multiplexing

    • In polymorphic multiplexing, we just connect the corresponding outputs of F1 and F2 by polymorphic multiplexers [5].


Polymorphic circuits1

POLYMORPHIC CIRCUITS

  • B.Polymorphic BDDs[5]

    • Terminal nodes can contain polymorphic logic functions.

    • Decision nodes are then implemented using standard multiplexers.


Polymorphic circuits2

POLYMORPHIC CIRCUITS

  • C.Evolutionary Approaches

    • Cartesian genetic programming (CGP)[11] can be seeded by a circuit created using polymorphic multiplexing or PolyBDDs and used to reduce the number of gates.

    • The method is applicable for small problem.


Direct evolution of polymorphic circuits using cgp

DIRECT EVOLUTION OF POLYMORPHIC CIRCUITSUSING CGP

  • Genetic Algorithm flow


Direct evolution of polymorphic circuits using cgp1

DIRECT EVOLUTION OF POLYMORPHIC CIRCUITSUSING CGP

  • CGP has been developed for circuit evolution by Miller and Thompson [11], [12].


Direct evolution of polymorphic circuits using cgp2

DIRECT EVOLUTION OF POLYMORPHIC CIRCUITSUSING CGP

  • b is the number of correct output bits obtained as response for all possible assignments to the inputs

  • z denotes the number of gates utilized in a offspring circuit


Proposed fitness evaluation for polymorphic circuits

PROPOSED FITNESS EVALUATION FOR POLYMORPHICCIRCUITS

  • The SAT-based Equivalence Checking


Proposed fitness evaluation for polymorphic circuits1

PROPOSED FITNESS EVALUATION FOR POLYMORPHICCIRCUITS


Proposed fitness evaluation for polymorphic circuits2

PROPOSED FITNESS EVALUATION FOR POLYMORPHICCIRCUITS


Proposed fitness evaluation for polymorphic circuits3

PROPOSED FITNESS EVALUATION FOR POLYMORPHICCIRCUITS


Results

RESULTS

  • Intel Xeon E5345 2.33 GHz

  • The MiniSAT 2 (version 070721) has been used as a SAT solver [18].

  • Benchmark LGSynth91


Results1

RESULTS


Results2

RESULTS


Results3

RESULTS


Results4

RESULTS


Results5

RESULTS


Conclusions

CONCLUSIONS

  • We proposed a new CGP-based method for evolutionary optimization of polymorphic circuits.

  • The new CGP-based method can reduce the number of gates by 20- 40% in comparison to conventional methods.


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