Fast computation of determination of the prime implicants by a novel near minimum minimization method

In this study proposed is an off-set-based direct-cover near-minimum minimization method for singleoutput Boolean functions represented in a sum-of-products form. To obtain the complete set of prime implicants including given on-cube (on-minterm), the proposed method uses off-cubes (off-minterms) expanded by this On-cube. The amount of temporary results produced by this method does not exceed the size of the offset. To make fast computation, we used logic operations instead of standard operations. Expansion off-cubes, commutative absorption operations and intersection operations are realized by logic operations for fast computation. The proposed minimization method is tested on several different kinds of problems and benchmarks results of which are compared with logic minimization program ESPRESSO. The results show that proposed algorithm obtains good results and faster than ESPRESSO.

[1]  Nripendra N. Biswas,et al.  An algorithm for multiple output minimization , 1989, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[2]  Tsutomu Sasao,et al.  Large-scale SOP minimization using decomposition and functional properties , 2003, Proceedings 2003. Design Automation Conference (IEEE Cat. No.03CH37451).

[3]  Tom Rhyne,et al.  An algorithm for identifying and selecting the primed implicants of a multiple-output Boolean function , 1988, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[4]  F. Basçiftçi,et al.  Simplification of Single-Output Boolean Functions by Exact Direct Cover Algorithm Based on Cube Algebra , 2007, EUROCON 2007 - The International Conference on "Computer as a Tool".

[5]  Arthur D. Friedman,et al.  Logical design of digital systems , 1975 .

[6]  Olivier Coudert,et al.  Two-level logic minimization: an overview , 1994, Integr..

[7]  F. Basçiftçi,et al.  An Off-Cubes Expanding Approach to the Problem of Separate Determination of the Essential Prime Implicants of the Single-Output Boolean Functions , 2007, EUROCON 2007 - The International Conference on "Computer as a Tool".

[8]  Robert K. Brayton,et al.  Two-Level Minimization of Multivalued Functions with Large Offsets , 1993, IEEE Trans. Computers.

[9]  Robert K. Brayton,et al.  Multi-level logic minimization using implicit don't cares , 1988, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[10]  T.,et al.  Minimization Algorithms for Multiple-Valued Programmable Logic Arrays , 2022 .

[11]  Tsutomu Sasao,et al.  Worst and Best Irredundant Sum-of-Products Expressions , 2001, IEEE Trans. Computers.

[12]  Edward J. McCluskey,et al.  Switching theory , 2003 .

[13]  Tsutomu Sasao.  EXMIN: a simplification algorithm for exclusive-OR-sum-of-products expressions for multiple-valued input two-valued output functions , 1990, Proceedings of the Twentieth International Symposium on Multiple-Valued Logic.

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

[15]  Tsutomu Sasao.  EXMIN2: a simplification algorithm for exclusive-OR-sum-of-products expressions for multiple-valued-input two-valued-output functions , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[16]  Giovanni De Micheli,et al.  Synthesis and Optimization of Digital Circuits , 1994 .

[17]  Tiziano Villa,et al.  Complexity of two-level logic minimization , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[18]  Fatih Başçiftçi,et al.  Boolean Functions Simplification Algorithm of O(n) Complexity , 2003 .

[19]  Robert K. Brayton,et al.  Reduced offsets for minimization of binary-valued functions , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

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