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An efficient NPN Boolean matching algorithm based on structural signature and Shannon expansion

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Abstract

An efficient pairwise Boolean matching algorithm for solving the problem of matching single-output specified Boolean functions under input negation and/or input permutation and/or output negation (NPN) is proposed in this paper. We present the structural signature (SS) vector, which comprises a first-order signature value, two symmetry marks, and a group mark. As a necessary condition for NPN Boolean matching, the SS is more effective than the traditional signature. A symmetry mark can distinguish symmetric variables and asymmetric variables and be used to search for multiple variable mappings in a single variable-mapping search operation, which reduces the search space significantly. Updating the SS vector via Shannon decomposition provides benefits in distinguishing unidentified variables, and the group mark and phase collision check can be used to discover incorrect variable mappings quickly, which also speeds up the NPN Boolean matching process. Using the algorithm proposed in this paper, we test both equivalent and non-equivalent matching speeds on the MCNC benchmark circuit sets and random circuit sets. In the experiment, our algorithm is shown to be 4.2 times faster than competitors when testing equivalent circuits and 172 times faster, on average, when testing non-equivalent circuits.

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Acknowledgements

We would like to thank the National Natural Science Foundation of China (Grant Nos. 619 61572109, 11371003) and the Special Fund for Bagui Scholars of Guangxi for their support for technology.

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Authors and Affiliations

  1. Big Data Research Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Juling Zhang, Guowu Yang & Yan Zhang

  2. Synopsys Inc., Mountain View, CA, USA

    William N. N. Hung

  3. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning, 530006, China

    Jinzhao Wu

Authors
  1. Juling Zhang
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  2. Guowu Yang
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  3. William N. N. Hung
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  4. Yan Zhang
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  5. Jinzhao Wu
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Correspondence to Jinzhao Wu.

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Zhang, J., Yang, G., Hung, W.N.N. et al. An efficient NPN Boolean matching algorithm based on structural signature and Shannon expansion. Cluster Comput 22 (Suppl 3), 7491–7506 (2019). https://doi.org/10.1007/s10586-018-1787-x

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