Doing two-level logic minimization 100 times faster

Two-level logic minimization consists in finding a minimal cost sum-of-products, i.e, disjunctive normal form, of a given Boolean function. This paper presents a new algorithm to solve this problem, and gives experimental evidences showing that it outperforms the leading minimizers of several orders of magnitude. We suspect that it may be possible to explain this improvement in performance theoretically, and hope that our empirical results will stimulate research along

[1]  George Markowsky,et al.  On the number of prime implicants , 1978, Discret. Math..

[2]  Tsutomu Sasao.  An application of multiple-valued logic to a design of programmable logic arrays , 1978, MVL '78.

[3]  Olivier Coudert,et al.  Fault tree analysis: 10/sup 20/ prime implicants and beyond , 1993, Annual Reliability and Maintainability Symposium 1993 Proceedings.

[4]  O. Coudert,et al.  A New Graph Based Prime Computation Technique , 1993 .

[5]  S. Yang,et al.  Logic Synthesis and Optimization Benchmarks User Guide Version 3.0 , 1991 .

[6]  S. Rudeanu.  Review: W. V. Quine, On Cores and Prime Implicants of Truth Functions , 1970 .

[7]  Saburo Muroga,et al.  Absolute Minimization of Completely Specified Switching Functions , 1991, IEEE Trans. Computers.

[8]  W. Quine.  On Cores and Prime Implicants of Truth Functions , 1959 .

[9]  Olivier Coudert,et al.  A New Viewpoint on Two-Level Logic Minimization , 1993, 30th ACM/IEEE Design Automation Conference.

[10]  R. Bryant.  Graph-Based Algorithms for Boolean Function Manipulation12 , 1986 .

[11]  E. McCluskey.  Minimization of Boolean functions , 1956 .

[12]  James F. Gimpel.  A Reduction Technique for Prime Implicant Tables , 1964, IEEE Trans. Electron. Comput..

[13]  Brian C. Williams,et al.  Diagnosing Multiple Faults , 1987, Artif. Intell..

[14]  Robert W. House,et al.  Gimpel's Reduction Technique Extended to the Covering Problem with Costs , 1967, IEEE Trans. Electron. Comput..

[15]  Willard Van Orman Quine,et al.  The Problem of Simplifying Truth Functions , 1952 .

[16]  Jean Christophe Madre,et al.  Proving circuit correctness using formal comparison between expected and extracted behaviour , 1988, 25th ACM/IEEE, Design Automation Conference.Proceedings 1988..

[17]  J. Shearer,et al.  Prime Implicants, Minimum Covers, and the Complexity of Logic Simplification , 1986, IEEE Transactions on Computers.

[18]  Alberto L. Sangiovanni-Vincentelli,et al.  Multiple-Valued Minimization for PLA Optimization , 1987, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[19]  I. B. Pyne,et al.  An Essay on Prime Implicant Tables , 1961 .

[20]  Olivier Coudert,et al.  A Logically Complete Reasoning Maintenance System Based on a Logical Constraint Solver , 1991, IJCAI.

[21]  Daniel L. Ostapko,et al.  MINI: A Heuristic Approach for Logic Minimization , 1974, IBM J. Res. Dev..

[22]  Jon Doyle,et al.  A Truth Maintenance System , 1979, Artif. Intell..

[23]  Shin-ichi Minato,et al.  Zero-Suppressed BDDs for Set Manipulation in Combinatorial Problems , 1993, 30th ACM/IEEE Design Automation Conference.

[24]  Olivier Coudert,et al.  Fault Tree Analysis: 1020 Prime Implicants and Beyond , 1993 .

[25]  Olivier Coudert,et al.  Implicit and incremental computation of primes and essential primes of Boolean functions , 1992, [1992] Proceedings 29th ACM/IEEE Design Automation Conference.

[26]  Alberto Sangiovanni-Vincentelli,et al.  Logic synthesis for vlsi design , 1989 .

[27]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[28]  Raymond J. Nelson,et al.  Review: W. V. Quine, The Problem of Simplifying Truth Functions , 1953 .

[29]  Robert K. Brayton,et al.  ESPRESSO-SIGNATURE: A New Exact Minimizer for Logic Functions , 1993, 30th ACM/IEEE Design Automation Conference.