Three parameters to find functional decompositions

Finding simple disjoint functional decompositions is a basic problem, but is generally time-consuming since there are nearly 2/sup n/ bipartitions of input variable. This paper introduces three parameters to find bipartitions of the input variables. It also defines "ideal random logic functions", and derives their properties. Experimental results using randomly generated functions and benchmark functions show the usefulness of the approach.

[1]  Giovanni De Micheli,et al.  Finding all simple disjunctive decompositions using irredundant sum-of-products forms , 1998, 1998 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (IEEE Cat. No.98CB36287).

[2]  Tsutomu Sasao,et al.  FPGA Design by Generalized Functional Decomposition , 1993 .

[3]  Sarma Vrudhula,et al.  EVBDD-based algorithms for integer linear programming, spectral transformation, and function decomposition , 1994, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[4]  Tsutomu Sasao,et al.  Switching Theory for Logic Synthesis , 1999, Springer US.

[5]  Tsutomu Sasao,et al.  Functional Decompositions Using an Automatic Test Pattern Generator and a Logic Simulator , 1999 .

[6]  Tsutomu Sasao.  Totally undecomposable functions: applications to efficient multiple-valued decompositions , 1999, Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329).

[7]  Mary Jane Irwin,et al.  Logic synthesis for field-programmable gate arrays , 1994, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[8]  Richard M. Karp,et al.  Minimization Over Boolean Graphs , 1962, IBM J. Res. Dev..

[9]  Yusuke Matsunaga.  An Exact and Efficient Algorithms for Disjunctive Decomposition , 1998 .

[10]  Elena Dubrova,et al.  On the relation between disjunctive decomposition and ROBDD variable ordering , 1997, 1997 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, PACRIM. 10 Years Networking the Pacific Rim, 1987-1997.

[11]  Peter Weiner,et al.  A Fast Algorithm for the Disjunctive Decomposition of Switching Functions , 1971, IEEE Transactions on Computers.

[12]  Stephen C. Crist.  Synthesis of Combinational Logic Using Decomposition and Probability , 1980, IEEE Transactions on Computers.

[13]  J. T. Proudfoot,et al.  Non-exhaustive method for identification of optimal variable orderings in the decomposition of complex logic functions , 1995 .

[14]  Hiroshi Sawada,et al.  Logic synthesis for look-up table based FPGAs using functional decomposition and support minimization , 1995, ICCAD.

[15]  H. A. Curtis,et al.  A new approach to The design of switching circuits , 1962 .

[16]  Tsutomu Sasao,et al.  On Bi-Decompositions of Logic Functions , 1997 .

[17]  Wen-Zen Shen,et al.  Lambda Set Selection in Roth-Karp Decomposition for LUT-Based FPGA Technology Mapping , 1995, 32nd Design Automation Conference.

[18]  V. Bertacco,et al.  The disjunctive decomposition of logic functions , 1997, 1997 Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[19]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[20]  Tsutomu Sasao,et al.  DECOMPOS : An integrated system for functional decomposition , 1998 .

[21]  L. Jozwiak,et al.  Efficient logic synthesis for FPGAs with functional decomposition based on information relationship measures , 1998, Proceedings. 24th EUROMICRO Conference (Cat. No.98EX204).

[22]  Tsutomu Sasao,et al.  Logic Synthesis and Optimization , 1997 .

[23]  Mariusz Rawski,et al.  Efficient input support selection for sub-functions in functional decomposition based on information relationship measures , 1999, Proceedings 25th EUROMICRO Conference. Informatics: Theory and Practice for the New Millennium.