2009
DOI: 10.1109/tcad.2009.2016547
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A Transform-Parametric Approach to Boolean Matching

Abstract: Abstract-In this paper, we face the problem of P-equivalence Boolean matching. We outline a formal framework that unifies some of the spectral and canonical form-based approaches to the problem.As a first major contribution, we show how these approaches are particular cases of a single generic algorithm, parametric with respect to a given linear transformation of the input function.As a second major contribution, we identify a linear transformation that can be used to significantly speed up Boolean matching wi… Show more

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Cited by 20 publications
(17 citation 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%
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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%
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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%
“…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%