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

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 firs...

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Veröffentlicht in:Cluster computing Jg. 22; H. Suppl 3; S. 7491 - 7506
Hauptverfasser: Zhang, Juling, Yang, Guowu, Hung, William N. N., Zhang, Yan, Wu, Jinzhao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.05.2019
Springer Nature B.V
Schlagworte:
Algorithms
Boolean
Boolean functions
Circuits
Classification
Codes
Computer Communication Networks
Computer Science
Decomposition
Equivalent circuits
Group theory
Matching
Operating Systems
Permutations
Processor Architectures
Searching
Symmetry
Variables
NPN equivalence
Boolean matching
Variable mapping
Structural signature vector
Shannon expansion
ISSN:1386-7857, 1573-7543
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1386-7857
1573-7543
DOI:10.1007/s10586-018-1787-x