Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Efficient data structures for Boolean functions
Discrete Mathematics - Special issue: trends in discrete mathematics
Formal Methods in System Design
Parity OBDDs cannot be handled efficiently enough
Information Processing Letters
On the Descriptive and Algorithmic Power of Parity Ordered Binary Decision Diagrams
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
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Ordered binary decision diagrams (OBDDs) and parity OBDDs are data structures representing Boolean functions. In addition, we study their generalization which we call parity AOBDDs, give their algebraic characterization and compare their minimal size to the size of parity OBDDs. We prove that the constraint that no arcs test conditions of type xi = 0 does not affect the node-size of parity (A)OBDDs and we give an efficient algorithm for finding such parity (A)OBDDs. We obtain a canonical form for parity OBDDs and discuss similar results for parity AOBDDs. Algorithms for minimization and transformation to the canonical form for parity OBDDs running in time O(S3) and space O(S2) or in time O(S3= log S) and space O(S3= log S) and an algorithm for minimization of parity AOBDDs running in time O(nS3) and space O(nS2) are presented (n is the number of variables, S is the number of vertices). All the results are extendable to case of shared parity (A)OBDDs -- data structures for representation of Boolean function sequences.