In this paper we initiate the study of proof systems where verification of proofs proceeds by NC0 circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC0 functions. Our results show that the answer ... more >>>

We study optimization versions of Graph Isomorphism. Given two graphs $G_1,G_2$, we are interested in finding a bijection $\pi$ from $V(G_1)$ to $V(G_2)$ that maximizes the number of matches (edges mapped to edges or non-edges mapped to non-edges). We give an $n^{O(\log n)}$ time approximation scheme that for any constant ... more >>>

We define instance compressibility for parametric problems in PH and PSPACE. We observe that

the problem \Sigma_{i}CircuitSAT of deciding satisfiability of a quantified Boolean circuit with i-1 alternations of quantifiers starting with an existential uantifier is complete for parametric problems in \Sigma_{i}^{p} with respect to W-reductions, and that analogously ... more >>>