Equivalence Problems for Circuits over Sets of Natural Numbers

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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, \({\rm \Pi^P_{2}}\) , 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.