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.
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Glaßer, C., Reitwießner, C., Travers, S., Waldherr, M. (2007). Satisfiability of Algebraic Circuits over Sets of Natural Numbers. In: Arvind, V., Prasad, S. (eds) FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2007. Lecture Notes in Computer Science, vol 4855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77050-3_21
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DOI: https://doi.org/10.1007/978-3-540-77050-3_21
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