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,\({\rm \Pi^P_{2}}\), 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.
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Glaßer, C., Herr, K., Reitwießner, C., Travers, S., Waldherr, M. (2007). Equivalence Problems for Circuits over Sets of Natural Numbers. In: Diekert, V., Volkov, M.V., Voronkov, A. (eds) Computer Science – Theory and Applications. CSR 2007. Lecture Notes in Computer Science, vol 4649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74510-5_15
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DOI: https://doi.org/10.1007/978-3-540-74510-5_15
Publisher Name: Springer, Berlin, Heidelberg
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