Satisfiability of algebraic circuits over sets of natural numbers

Authors:
Christian Glaßer;Christian Reitwießner;Stephen Travers;Matthias Waldherr
Affiliations:
Theoretische Informatik, Julius-Maximilians-Universität Würzburg, Germany;Theoretische Informatik, Julius-Maximilians-Universität Würzburg, Germany;Theoretische Informatik, Julius-Maximilians-Universität Würzburg, Germany;Theoretische Informatik, Julius-Maximilians-Universität Würzburg, Germany
Venue:
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Year:
2007

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Abstract

We investigate the complexity of satisfiability problems for {∪, ∩, -, +, ×}-circuits computing sets of natural numbers. These problems are a natural generalization of membership problems for expressions and circuits studied by Stockmeyer and Meyer (1973) and McKenzie and Wagner (2003). Our work shows that satisfiability problems capture a wide range of complexity classes like NL, P, NP, PSPACE, and beyond. We show that in several cases, satisfiability problems are harder than membership problems. In particular, we prove that testing satisfiability for {∩, +, ×}- circuits already is undecidable. In contrast to this, the satisfiability for {∪, +, ×}-circuits is decidable in PSPACE.