Equivalence problems for circuits over sets of natural numbers

Authors:
Christian Glaßer;Katrin Herr;Christian Reitwießner;Stephen Travers;Matthias Waldherr
Affiliations:
Julius-Maximilians-Universität Würzburg, Theoretische Informatik, Germany;Julius-Maximilians-Universität Würzburg, Theoretische Informatik, Germany;Julius-Maximilians-Universität Würzburg, Theoretische Informatik, Germany;Julius-Maximilians-Universität Würzburg, Theoretische Informatik, Germany;Julius-Maximilians-Universität Würzburg, Theoretische Informatik, Germany
Venue:
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
Year:
2007

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Abstract

We investigate the complexity of equivalence problems for {∪ ∩ -,+,×}-circuits computing sets of natural numbers. These problems were first introduced by Stockmeyer and Meyer (1973). We continue this line of research and give a systematic characterization of the complexity of equivalence problems over sets of natural numbers. Our work shows that equivalence problems capture a wide range of complexity classes like NL, C=L, P,Π2P, PSPACE, NEXP, and beyond. McKenzie and Wagner (2003) studied related membership problems for circuits over sets of natural numbers. Our results also have consequences for these membership problems: We provide an improved upper bound for the case of {∪, ∩,-,+, ×}-circuits.