SAT-Based Equivalence Checking Based on Circuit Partitioning and Special Approaches for Conflict Clause Reuse

This paper presents a new SAT-based CEC methodology for the verification of circuits with structural dependence. This methodology is based on circuit partitioning and special approaches for conflict clauses reuse, reducing highly the CEC problem complexity. Using this methodology it is possible to improve the overall verification time of similar and dissimilar circuits. For instance, for similar multiplier circuits it was possible to check equivalence up to 37 times 37 bit without any circuit topological information in nearly 40 minutes. For dissimilar circuits, the proposed methodology is able to check equivalence up to 24 times 24 bit in one hour overcoming the BDD-based approaches that using cutpoints cannot check beyond a 12 times 12 bit multiplier with reasonable time limit.

[1]  Michael S. Hsiao,et al.  Enhancing SAT-based equivalence checking with static logic implications , 2003, Eighth IEEE International High-Level Design Validation and Test Workshop.

[2]  Rolf Drechsler,et al.  BDD-based verification of scalable designs , 2003, Eighth IEEE International High-Level Design Validation and Test Workshop.

[3]  Daniel D. Gajski,et al.  High ― Level Synthesis: Introduction to Chip and System Design , 1992 .

[4]  Joao Marques-Silva Algorithms for Satisfiability in Combinational Circuits Based on Backtrack Search and Recursive Learning , 1999 .

[5]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[6]  Eugene Goldberg On equivalence checking and logic synthesis of circuits with a common specification , 2005, ACM Great Lakes Symposium on VLSI.

[7]  Jerry R. Burch,et al.  Using bdds to verify multipliers , 1991, 28th ACM/IEEE Design Automation Conference.

[8]  Y. Novikov,et al.  Equivalence Checking of Dissimilar Circuits , 2003 .

[9]  Randal E. Bryant,et al.  Verification of arithmetic circuits using binary moment diagrams , 2001, International Journal on Software Tools for Technology Transfer.

[10]  Dhiraj K. Pradhan,et al.  Recursive learning: a new implication technique for efficient solutions to CAD problems-test, verification, and optimization , 1994, The IEEE International Symposium on Circuits and Systems, 2003. Tutorial Guide: ISCAS 2003..

[11]  Minh N. Do,et al.  Youn-Long Steve Lin , 1992 .

[12]  Kwang-Ting Cheng,et al.  A circuit SAT solver with signal correlation guided learning , 2003, 2003 Design, Automation and Test in Europe Conference and Exhibition.

[13]  Robert K. Brayton,et al.  Using SAT for combinational equivalence checking , 2001, Proceedings Design, Automation and Test in Europe. Conference and Exhibition 2001.

[14]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[15]  Daniel Brand Verification of large synthesized designs , 1993, ICCAD.

[16]  Armin Biere,et al.  A survey of recent advances in SAT-based formal verification , 2005, International Journal on Software Tools for Technology Transfer.

[17]  Andreas Kuehlmann,et al.  Equivalence checking using cuts and heaps , 1997, DAC.

[18]  Randal E. Bryant,et al.  Verification of Arithmetic Circuits with Binary Moment Diagrams , 1995, 32nd Design Automation Conference.

[19]  Dominik Stoffel,et al.  Equivalence checking of arithmetic circuits on the arithmetic bit level , 2004, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[20]  Randal E. Bryant,et al.  On the Complexity of VLSI Implementations and Graph Representations of Boolean Functions with Application to Integer Multiplication , 1991, IEEE Trans. Computers.

[21]  Wolfgang Kunz HANNIBAL: an efficient tool for logic verification based on recursive learning , 1993, ICCAD.

[22]  Ted Stanion Implicit verification of structurally dissimilar arithmetic circuits , 1999, Proceedings 1999 IEEE International Conference on Computer Design: VLSI in Computers and Processors (Cat. No.99CB37040).