A Transform-Parametric Approach to Boolean Matching

Agosta, Giovanni; Bruschi, Francesco; Pelosi, Gerardo; Sciuto, D.

doi:10.1109/tcad.2009.2016547

Cited by 20 publications

(17 citation statements)

References 19 publications

(45 reference statements)

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“…Comparison of average runtimes on the non-equivalent random circuits gorithm finds some possible transformations, but none of these transformations satisfy f (T X) = g(X) or f (T X) = g(X). In our testing, almost all non-equivalent circuit functions belong to (1), and a handful of non-equivalent circuits belong to (2). Our algorithm spends considerable time generating circuit functions that belong to (3).…”

Section: Resultsmentioning

confidence: 99%

“…V f ={(0, 0, 2, 0, 1),(11, 8, 2, 1, 1),(0, 0, -1, -1, 0),(8, 11, 2, 1, 1),(0, 0, 2, 0, 1),(10, 9, -1, -1, 3),(7, 12, -1, -1, 2)} V g ={(0, 0, 2, 0, 1),(7, 12, -1, -1, 2),(0, 0, 2, 0, 1),(11, 8, 2, 3, 1), (11,8,2,3,1),(0, 0, -1, -1, 0),(10, 9, -1, -1, 3)} From the above updated SS vectors, we know that these two SS vectors are the same and that one single symmetrymapping set (S 1 = {1 → 3}) and two single-mapping sets (χ 5 = {5 → 6 − 0} and χ 6 = {6 → 1 − 0}) exist. Procedure 2 adds variable mappings 1 → 3 − 0, 3 → 4 − 1, 5 → 6 − 0 and 6 → 1 − 0 to the transformation tree.…”

Section: Boolean Matchingmentioning

confidence: 99%

“…Damiani and Selchenko [5] used decomposition trees to create the Boolean function representative. Agosta et al [1] combined the spectral and canonical forms to exploit a transformparametric approach that could match Boolean functions of up to 20 variables, but this method considers only the input permutation. The authors of [13] proposed a fast Boolean function NPN classification using canonical forms, in which a Boolean function is represented by a truth table.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Boolean Matchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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“…A common approach of NPN classification is to construct a canonical form for a Boolean function , and use this canonical form as the representative of the equivalence class belongs to. There are several NPN canonical forms, such as the function with the smallest truth table representation [10] [11], or with the smallest spectrum representation in the NPN equivalence class [12]- [14].…”

Section: Introductionmentioning

confidence: 99%

Fast Adjustable NPN Classification using Generalized Symmetries

Zhou

Wang

Zhao³

et al. 2018

2018 28th International Conference on Field Programmable Logic and Applications (FPL)

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NPN classification of Boolean functions is a powerful technique used in many logic synthesis and technology mapping tools in FPGA design flows. Computing the canonical form of a function is the most common approach of Boolean function classification. In this paper, a novel algorithm for computing NPN canonical form is proposed. By exploiting symmetries under different phase assignments and higher-order symmetries of Boolean functions, the search space of NPN canonical form computation is pruned and the runtime is dramatically reduced. The algorithm can be adjusted to be a slow exact algorithm or a fast heuristic algorithm with lower quality. For exact classification, the proposed algorithm achieves a 30× speedup compared to a state-of-the-art algorithm. For heuristic classification, the proposed algorithm has similar performance as the state-of-the-art algorithm with a possibility to trade runtime for quality.

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“…It is an important subject both in theory, see, e.g., [7,4], and in practice, e.g., [5,8,17,14]. However, most prior efforts on Boolean matching focused mainly on single-output functions, e.g., [5,23,22,1,3,2,24], and very few on multiple-output functions, e.g., [13]. This bias can be attributed to the fact that single-output Boolean matching is more fundamental in theory, easier in computation, and more pervasive in applications.…”

Section: Introductionmentioning

confidence: 99%

Boolean matching of function vectors with strengthened learning

Lai¹,

Jiang²,

Wang³

2010

2010 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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Boolean matching for multiple-output functions determines whether two given (in)completely-specified function vectors can be identical to each other under permutation and/or negation of their inputs and outputs. Despite its importance in design rectification, technology mapping, and other logic synthesis applications, there is no much direct study on this subject due to its generality and consequent computational complexity. This paper extends our prior Boolean matching decision procedure BooM to consider multiple-output functions. Through conflict-driven learning and partial assignment reduction, Boolean matching in the most general setting can still be accomplishable even when all other techniques lose their foundation and become unapplicable. Experiments demonstrate the indispensable power of strengthened learning for practical applications.

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A Transform-Parametric Approach to Boolean Matching

Cited by 20 publications

References 19 publications

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

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

Fast Adjustable NPN Classification using Generalized Symmetries

Boolean matching of function vectors with strengthened learning

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