# Satisfiability of algebraic circuits over sets of natural numbers

@article{Glaer2010SatisfiabilityOA, title={Satisfiability of algebraic circuits over sets of natural numbers}, author={Christian Gla{\ss}er and Christian Reitwie{\ss}ner and Stephen D. Travers and Matthias Waldherr}, journal={Discret. Appl. Math.}, year={2010}, volume={158}, pages={1394-1403} }

We investigate the complexity of satisfiability problems for {@?,@?,^-,+,x}-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) [10] and McKenzie and Wagner (2003) [8]. Our work shows that satisfiability problems capture a wide range of complexity classes such as NL, P, NP, PSPACE, and beyond. We show that in several cases, satisfiability problems are harder than… Expand

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