Equivalence Problems for Circuits over Sets of Natural Numbers

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, ΠP 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 improved upper bounds for the cases of {∪, ∩, − , +, ×}- and {∩, +, ×}-circuits. Classification: Computational and structural complexity; Combinational Circuits; Algorithms

• Type: Conference
• Year: 2007
• Where: CSR
• Authors: Christian Glaßer, Katrin Herr, Christian Reitwießner, Stephen D. Travers, Matthias Waldherr
• Keywords: CSR 2007, Equivalence Problems, Natural Numbers, ×}-circuits Computing Sets