Formal Methods in System Design
, Volume 8, Issue 3, pp 273282
First online:
Mod2OBDDs—A data structure that generalizes EXORsumofproducts and ordered binary decision diagrams
 Jordan GergovAffiliated withMaxPlanckInstitut für Informatik
 , Christoph MeinelAffiliated withFachbereich IVInformatik, Universität Trier
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We present a data structure for Boolean manipulationthe Mod2OBDDsthat considerably extends ESOPs (EXORsumofproducts) as well as OBDDs (ordered binary decision diagrams). There are Boolean functions of practical interest which have exponential size optimal ESOPs (even multilevel EXORexpressions) and/or OBDDs that can be represented by (low degree) polynomial size Mod2OBDDs.
We show that Boolean manipulation tasks such as apply operation, quantification, composition can be performed with Mod2OBDDs at least as efficient as with OBDDs. Indeed, since the size of a minimal Mod2OBDDrepresentation of a Boolean function is, in general, smaller (sometimes even exponentially smaller) than the size of an optimal OBDDrepresentation, the increase in efficiency is considerable. Moreover, EXORoperations as well as complementations can be performed in constant timeO (1).
However, the price of constant time EXORapply operations is the canonicity of the Mod2OBDDrepresentation. In order to allow in spite of this fact efficient analysis of Mod2OBDDs we present a fast probabilistic equivalence test with onesided error probability for Mod2OBDDs (and, hence, for ESOPs) which performs only linear many arithmetic operations.
Keywords
data structures for Boolean functions BDDs verification EXOR expressions Title
 Mod2OBDDs—A data structure that generalizes EXORsumofproducts and ordered binary decision diagrams
 Journal

Formal Methods in System Design
Volume 8, Issue 3 , pp 273282
 Cover Date
 199605
 DOI
 10.1007/BF00709139
 Print ISSN
 09259856
 Online ISSN
 15728102
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 data structures for Boolean functions
 BDDs
 verification
 EXOR expressions
 Industry Sectors
 Authors

 Jordan Gergov ^{(1)}
 Christoph Meinel ^{(2)}
 Author Affiliations

 1. MaxPlanckInstitut für Informatik, Im Stadtwald, D66123, Saarbrücken, Germany
 2. Fachbereich IVInformatik, Universität Trier, D54286, Trier, Germany