Nondeterministic ordered binary decision diagrams with repeated tests and various modes of acceptance

Authors:
Henrik Brosenne;Matthias Homeister;Stephan Waack
Affiliations:
Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3--5, 37073 Göttingen, Germany;Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, Lotzestr. 16--18, 37083 Göttingen, Germany;Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, Lotzestr. 16--18, 37083 Göttingen, Germany
Venue:
Information Processing Letters
Year:
2006

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Abstract

Ordered binary decision diagrams with repeated tests are considered both in complexity theory and in applications. Bollig et al. have proved in [B. Bollig, M. Sauerhoff, D. Sieling, I. Wegener, Hierarchy theorems of kOBDDs and kIBDDs, Theoret. Comput. Sci. 205 (1998) 45-60] a tight hierarchy result for the classes of functions representable by k layers of polynomial-size deterministic ordered binary decision diagrams. In this paper the nondeterministic case is investigated, where the layers are driven by one and the same variable ordering. For k being a constant, it is shown that for the existential, the parity-, and the majority acceptance mode the analogous hierarchy collapses.