Evolutionary Synthesis of Logic Circuits Using Information Theory

In this paper, we propose the use of Information Theory as thebasis for designing a fitness function for Boolean circuit designusing Genetic Programming. Boolean functions are implemented byreplicating binary multiplexers. Entropy-based measures, such asMutual Information and Normalized Mutual Information areinvestigated as tools for similarity measures between the targetand evolving circuit. Three fitness functions are built over aprimitive one. We show that the landscape of Normalized MutualInformation is more amenable for being used as a fitness functionthan simple Mutual Information. The evolutionary synthesizedcircuits are compared to the known optimum size. A discussion ofthe potential of the Information-Theoretical approach is given.

[1]  Pramod K. Varshney,et al.  Application of information theory to the construction of efficient decision trees , 1982, IEEE Trans. Inf. Theory.

[2]  Claudio Moraga,et al.  Information theory method for flexible network synthesis , 2001, Proceedings 31st IEEE International Symposium on Multiple-Valued Logic.

[3]  Carlos A. Coello Coello,et al.  Extracting and re-using design patterns from genetic algorithms using case-based reasoning , 2003 .

[4]  Jim Tørresen,et al.  A Scalable Approach to Evolvable Hardware , 2002, Genetic Programming and Evolvable Machines.

[5]  J. H. Herzog,et al.  Genetic programming and its applications to the synthesis of digital logic , 1997, 1997 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, PACRIM. 10 Years Networking the Pacific Rim, 1987-1997.

[6]  Bernd Becker,et al.  On the generation of multiplexer circuits for pass transistor logic , 2000, DATE '00.

[7]  J. Ross Quinlan,et al.  Learning Efficient Classification Procedures and Their Application to Chess End Games , 1983 .

[8]  Colin Studholme,et al.  An overlap invariant entropy measure of 3D medical image alignment , 1999, Pattern Recognit..

[9]  Stefan Droste.  Efficient Genetic Programming for Finding Good Generalizing Boolean Functions , 1998 .

[10]  Julian Francis Miller,et al.  Principles in the Evolutionary Design of Digital Circuits—Part II , 2000, Genetic Programming and Evolvable Machines.

[11]  Carlos A. Coello Coello,et al.  A genetic programming approach to logic function synthesis by means of multiplexers , 1999, Proceedings of the First NASA/DoD Workshop on Evolvable Hardware.

[12]  Claudio Moraga,et al.  Evolutionary multi-level network synthesis in given design style , 2000, Proceedings 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2000).

[13]  Alan D. Christiansen,et al.  Towards automated evolutionary design of combinational circuits , 2000, Comput. Electr. Eng..

[14]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[15]  Charles F. Hockett,et al.  A mathematical theory of communication , 1948, MOCO.

[16]  A. Lloris,et al.  Using decision trees for the minimization of multiple-valued functions , 1993 .

[17]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[18]  P. Varshney,et al.  Application of information theory to switching function minimisation , 1990 .

[19]  Guy Marchal,et al.  Multimodality image registration by maximization of mutual information , 1997, IEEE Transactions on Medical Imaging.

[20]  C. Scholl,et al.  On the generation of multiplexer circuits for pass transistor logic , 2000, Proceedings Design, Automation and Test in Europe Conference and Exhibition 2000 (Cat. No. PR00537).

[21]  A. H. Aguirre,et al.  AUTOMATED DESIGN OF COMBINATIONAL LOGIC CIRCUITS USING GENETIC ALGORITHMS , 2022 .

[22]  Rolf Drechsler,et al.  A Genetic Algorithm for Minimization of Fixed Polarity Reed-Muller Expressions , 1995, ICANNGA.

[23]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[24]  Sushil J. Louis,et al.  Genetic algorithms as a computational tool for design , 1993 .

[25]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[26]  Julian Francis Miller,et al.  Scalability problems of digital circuit evolution evolvability and efficient designs , 2000, Proceedings. The Second NASA/DoD Workshop on Evolvable Hardware.

[27]  Alan D. Christiansen,et al.  Automated Design of Combinational Logic Circuits by Genetic Algorithms , 1997, ICANNGA.

[28]  A. H. Aguirre,et al.  Gate-level synthesis of Boolean functions using binary multiplexers and genetic programming , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[29]  Claudio Moraga,et al.  Application of design style in evolutionary multi-level networks synthesis , 2000, Proceedings of the 26th Euromicro Conference. EUROMICRO 2000. Informatics: Inventing the Future.

[30]  Hitoshi Iba,et al.  Gate-Level Evolvable Hardware: Empirical Study and Application , 1997 .

[31]  Julian F. Miller,et al.  Evolvable Systems: From Biology to Hardware - 9th International Conference, ICES 2010, York, UK, September 6-8, 2010. Proceedings , 2010, ICES.

[32]  Carlos A. Coello Coello,et al.  GA-Based Learning of kDNFns Boolean Formulas , 2001, ICES.

[33]  Rolf Drechsler,et al.  Binary Decision Diagrams - Theory and Implementation , 1998 .

[34]  Tatiana Kalganova,et al.  Bidirectional incremental evolution in extrinsic evolvable hardware , 2000, Proceedings. The Second NASA/DoD Workshop on Evolvable Hardware.

[35]  Rolf Drechsler,et al.  Learning Heuristics for OBDD Minimization by Evolutionary Algorithms , 1996, PPSN.

[36]  Guy Marchal,et al.  Multi-modality image registration by maximization of mutual information , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[37]  Sushil J. Louis,et al.  Solving Similar Problems Using Genetic Algorithms and Case-Based Memory , 1997, ICGA.

[38]  Bernd Becker,et al.  Fast OFDD based minimization of fixed polarity Reed-Muller expressions , 1994, EURO-DAC '94.

[39]  Paul J. Layzell,et al.  Explorations in design space: unconventional electronics design through artificial evolution , 1999, IEEE Trans. Evol. Comput..