Boolean matching of function vectors with strengthened learning

Lai, Chih-Fan; Jiang, Jie-Hong R.; Wang, Kuo-Hua

doi:10.1109/iccad.2010.5654215

Cited by 10 publications

(5 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Reference [24] introduced the Bloom filter to the SAT-based Boolean matching method to solve insufficient storage space. The authors of Reference [25] and Reference [26] used incremental and dynamic learning approaches to solve the Boolean matching problem, respectively. Through conflict-driven dynamic learning and abstraction, Reference [27] effectively pruned infeasible matching solutions.…”

Section: Related Workmentioning

confidence: 99%

“…The authors of Reference [25] and Reference [26] used incremental and dynamic learning approaches to solve the Boolean matching problem, respectively. Through conflict-driven dynamic learning and abstraction, Reference [27] effectively pruned infeasible matching solutions. Reference [28] created a treelike logic network that represented the decomposition properties of Boolean functions and implemented a tree-based Boolean matching algorithm.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

A Heuristic Boolean NPN Equivalent Matching Verification Method Based on Shannon Decomposition

et al. 2022

View full text Add to dashboard Cite

In this paper, we describe a new verification method to accelerate the input negation and/or input permutation and/or output negation (NPN) Boolean matching for a single-output completely specified Boolean function. Through research on the Boolean Shannon decomposition binary tree, we prove that the signature vectors of the left child node and right child node are complementary relative to the signature vector of the parent node. We introduce an independent variable check to speed up the detection of candidate transformation. The proposed approach utilises this complementarity, a symmetry check, an independent variable check and a phase collision check, which can quickly verify whether the candidate transformation obtained in the detection of the candidate transformation of the Boolean matching process is accurate. We perform experiments on two types of Boolean function sets. One type consists of Boolean functions from randomly generated circuits. The other is exported from the Microelectronics Center of North Carolina (MCNC) benchmark. The experimental results show that the average runtime of our algorithm is 68.8% faster than those in on two randomly generated circuits and 51% faster than those in when tested on the MCNC benchmark circuit set. Therefore, the experimental results demonstrate the effectiveness of the proposed method.INDEX TERMS Boolean matching, NPN equivalence, Shannon expansion, Shannon decomposition binary tree, signature vector.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

A Heuristic Boolean NPN Equivalent Matching Verification Method Based on Shannon Decomposition

et al. 2022

View full text Add to dashboard Cite

show abstract

“…In [23], the authors studied NPN Boolean matching using a Walsh Spectral Decision Diagram, and achieved an efficiency higher than that of Luks' hypergraph method. Lai et al [24] utilized a conflict-driven learning method to solve the multiple-output Boolean function matching problem.…”

Section: Related Workmentioning

confidence: 99%

“…Procedure 1 computes |f | = 46 and assigns a positive phase to f . Then, it computes the 1 st DC signature value of all the variables of f , and the results are {(16,28), (16,28), (30,28), (22,44), (24,44), (15,32), (30,28)}. The variables x 3 , x 5 and x 7 are positive, and the others are negative.…”

Section: Procedures 1 Compute Canonical Formmentioning

confidence: 99%

A Canonical-based NPN Boolean Matching Algorithm Utilizing Boolean Difference and Cofactor Signature

Zhang

Yang

Hung

et al. 2017

Preprint

View full text Add to dashboard Cite

This paper presents a new compact canonical-based algorithm to solve the problem of single-output completely specified NPN Boolean matching. We propose a new signature vector Boolean difference and cofactor (DC) signature vector. Our algorithm utilizes the Boolean difference, cofactor signature and symmetry properties to search for canonical transformations. The use of symmetry and Boolean difference notably reduces the search space and speeds up the Boolean matching process compared to the algorithm proposed in [1]. We tested our algorithm on a large number of circuits. The experimental results showed that the average runtime of our algorithm 37% higher and its average search space 67% smaller compared to [1] when tested on general circuits.

show abstract

“…The authors of [27] proposed a generalized Boolean symmetry and applied it to PP Boolean matching for large circuits. Lai et al [28] proposed Boolean matching with strengthened learning.…”

mentioning

confidence: 99%

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

et al. 2018

View full text Add to dashboard Cite

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. Two Boolean functions, f and g, may be equivalent when they have the same SS vector. 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. The experimental results show that our approach is highly effective at solving the NPN Boolean matching problem.

show abstract

Boolean matching of function vectors with strengthened learning

Cited by 10 publications

References 24 publications

A Heuristic Boolean NPN Equivalent Matching Verification Method Based on Shannon Decomposition

A Heuristic Boolean NPN Equivalent Matching Verification Method Based on Shannon Decomposition

A Canonical-based NPN Boolean Matching Algorithm Utilizing Boolean Difference and Cofactor Signature

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

Contact Info

Product

Resources

About