Factoring and recognition of read-once functions using cographs and normality and the readability of functions associated with partial k-trees

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Abstract

An approach for factoring general boolean functions was described in Golumbic and Mintz [Factoring logic functions using graph partitioning, in: Proceedings of IEEE/ACM International Conference on Computer Aided Design, November 1999, pp. 195-198] and Mintz and Golumbic [Factoring Boolean functions using graph partitioning, Discrete Appl. Math. 149 (2005) 131-153] which is based on graph partitioning algorithms. In this paper, we present a very fast algorithm for recognizing and factoring read-once functions which is needed as a dedicated factoring subroutine to handle the lower levels of that factoring process. The algorithm is based on algorithms for cograph recognition and on checking normality. For non-read-once functions, we investigate their factoring based on their corresponding graph classes. In particular, we show that if a function F is normal and its corresponding graph is a partial k-tree, then F is a read 2k function and a read 2k formula for F can be obtained in polynomial time. © 2006 Elsevier B.V. All rights reserved.

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Golumbic, M. C., Mintz, A., & Rotics, U. (2006). Factoring and recognition of read-once functions using cographs and normality and the readability of functions associated with partial k-trees. Discrete Applied Mathematics, 154(10), 1465–1477. https://doi.org/10.1016/j.dam.2005.09.016

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