Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Zero-suppressed BDDs for set manipulation in combinatorial problems
DAC '93 Proceedings of the 30th international Design Automation Conference
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Integration, the VLSI Journal
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ICCAD '94 Proceedings of the 1994 IEEE/ACM international conference on Computer-aided design
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IEEE Transactions on Computers
Dynamic variable ordering for ordered binary decision diagrams
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Detection of symmetry of Boolean functions represented by ROBDDs
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Journal of the ACM (JACM)
Communications of the ACM
Logic Synthesis and Verification Algorithms
Logic Synthesis and Verification Algorithms
Generalized symmetries in boolean functions
Proceedings of the 2000 IEEE/ACM international conference on Computer-aided design
ICCD '92 Proceedings of the 1991 IEEE International Conference on Computer Design on VLSI in Computer & Processors
Technology mapping using boolean matching and don't care sets
EURO-DAC '90 Proceedings of the conference on European design automation
BDD minimization using symmetries
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Fast computation of symmetries in Boolean functions
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Symmetric item set mining based on zero-suppressed BDDs
DS'06 Proceedings of the 9th international conference on Discovery Science
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Detecting symmetries is crucial to logic synthesis, technology mapping, detecting function equivalence under unknown input correspondence, and ROBDD minimization. State-of-the-art is represented by Mishchenko's algorithm. In this paper we present an efficient anytime algorithm for detecting symmetries in Boolean functions represented as ROBDDs, that output pairs of symmetric variables until a prescribed time bound is exceeded. The algorithm is complete in that given sufficient time it is guaranteed to find all symmetric pairs. The complexity of this algorithm is in O(n4 + n|G| + |G|3) where n is the number of variables and |G| the number of nodes in the ROBDD, and it is thus competitive with Mishchenko's O (|G|3) algorithm in the worst-case since n ≪ |G|. However, our algorithm performs significantly better because the anytime approach only requires lightweight data structure support and it offers unique opportunities for optimization.