A New Graph Based Prime Computation Technique

Computing prime and essential primes of Boolean functions is a problem that has applications in many different areas of computer science including computer design [2, 9], automated reasoning [12], and reliability analysis [8]. Though much effort has been spent on this problem over the last decades, all the prime computation techniques that have been developed so far are of limited power because they all manipulate sets of primes explicitly. This chapter presents a new prime computation procedure that overcomes this limitation because its complexity is not related to the number of primes to be computed but to the sizes of the graphs used to represent the sets of primes implicitly.

[1]  Robert K. Brayton,et al.  Implicit state enumeration of finite state machines using BDD's , 1990, 1990 IEEE International Conference on Computer-Aided Design. Digest of Technical Papers.

[2]  Olivier Coudert,et al.  Symbolic prime generation for multiple-valued functions , 1992, [1992] Proceedings 29th ACM/IEEE Design Automation Conference.

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

[4]  F. Brglez,et al.  A neutral netlist of 10 combinational benchmark circuits and a target translator in FORTRAN , 1985 .

[5]  S. C. Kleene,et al.  Introduction to Metamathematics , 1952 .

[6]  Olivier Coudert,et al.  A new method to compute prime and essential prime implicants of Boolean functions , 1992 .

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

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

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

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

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

[12]  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.