Algebraic and Uniqueness Properties of Parity Ordered Binary Decision Diagrams and Their Generalization
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 x i = 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(S 3) and space O(S 2) or in time O(S 3/logS) and space O(S 3/ logS) and an algorithm for minimization of parity AOBDDs running in time O(nS 3) and space O(nS 2) 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.
KeywordsBoolean Function Canonical Form Uniqueness Condition Binary Decision Diagram Shared Parity
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