Frontiers of Feasible and Probabilistic Feasible Boolean Manipulation with Branching Programs

Abstract

Extended Abstract Abstract. A central issue in the solution of many computer aided design problems is to nd concise representations for circuit designs and their functional speciication. Recently, a restricted type of branching programs (OBDDs) proved to be extremely useful for representing Boolean functions for various CAD applications Bry92]. Unfortunatelly, many circuits of practical interest provably require OBDD{representations of exponential size. In the following we systematically study the question up to what extend more concise BP-representations can be successfully used in symbolic Boolean manipulation, too. We prove, in very general settings, { The frontier of eecient (deterministic) symbolic Boolean manipulation on the basis of BP{representations are read{once{only branching programs (BP1). { The frontier of eecient probabilistic manipulation with BP{based data structures are parity read{once{only branching programs ({ BP1). Since BP1s and {BP1s are generally more (sometimes even exponentially more) succinct than OBDD{representations our results make accessible more succinct types of BPs as data structures for practical purposes. (A BP1{package as well as a {BP1{package are in preparation.) On the other side, our results together with the results obtained in GM92] show that the solution of basic tasks in Boolean manipulation for less restricted BP-types becomes NP{hard.

DOI: 10.1007/3-540-56503-5_57

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Cite this paper

@inproceedings{Gergov1993FrontiersOF, title={Frontiers of Feasible and Probabilistic Feasible Boolean Manipulation with Branching Programs}, author={Jordan Gergov and Christoph Meinel}, booktitle={STACS}, year={1993} }