Arithmetic Circuits Verification without Looking for Internal Equivalences

In this paper, we propose a novel approach to extract a network of half adders from the gate-level net-list of an addition circuit while no internal equivalences exist. The technique begins with a gate-level net-list and tries to map it into word-level adders based on an efficient bit-level adder representation. It will be shown that the proposed technique is suitable for several gate-level architectures of multipliers, as it extracts adder components in a step-wise method. This approach can also be generalized to other arithmetic circuits. In order to evaluate the effectiveness of our approach, we run it on several arithmetic circuits and compare experimental results with those of contemporary techniques.

[1]  Markus Wedler,et al.  Normalization at the arithmetic bit level , 2005, Proceedings. 42nd Design Automation Conference, 2005..

[2]  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.

[3]  Shuzo Yajima,et al.  Efficient construction of binary moment diagrams for verifying arithmetic circuits , 1995, Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[4]  Shi-Yu Huang,et al.  Formal Equivalence Checking and Design Debugging , 1998 .

[5]  Masahiro Fujita,et al.  LTED : A Canonical and Compact Hybrid Word-Boolean Representation as a Formal Model for Hardware / Software Co-designs , 2007 .

[6]  D. Brand Verification of large synthesized designs , 1993, Proceedings of 1993 International Conference on Computer Aided Design (ICCAD).

[7]  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).

[8]  Masahiro Fujita,et al.  Verification of Arithmetic Circuits by Comparing Two Similar Circuits , 1996, CAV.

[9]  Shuzo Yajima,et al.  Efficient construction of binary moment diagrams for verifying arithmetic circuits , 1995, ICCAD.

[10]  Dominik Stoffel,et al.  Verification of integer multipliers on the arithmetic bit level , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[11]  Dominik Stoffel,et al.  Reasoning in Boolean Networks - Logic Synthesis and Verification Using Testing Techniques , 1997, Frontiers in electronic testing.

[12]  Priyank Kalla,et al.  Equivalence verification of polynomial datapaths with fixed-size bit-vectors using finite ring algebra , 2005, ICCAD-2005. IEEE/ACM International Conference on Computer-Aided Design, 2005..

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

[14]  Priyank Kalla,et al.  Equivalence verification of arithmetic datapaths with multiple word-length operands , 2006, Proceedings of the Design Automation & Test in Europe Conference.