We investigate the computational complexity of the Boolean Isomorphism problem (BI):
on input of two Boolean formulas F and G decide whether there exists a permutation of
the variables of G such that F and G become equivalent.

Our main result is a one-round interactive proof ... more >>>

We consider a class, denoted APP, of real-valued functions
f:{0,1}^n\rightarrow [0,1] such that f can be approximated, to
within any epsilon>0, by a probabilistic Turing machine running in
time poly(n,1/epsilon). We argue that APP can be viewed as a
generalization of BPP, and show that APP contains a natural
complete ... more >>>

We prove that the exact versions of the domatic number problem are complete
for the levels of the boolean hierarchy over NP. The domatic number
problem, which arises in the area of computer networks, is the problem of
partitioning a given graph into a maximum number ... more >>>

This paper surveys some of the work that was inspired by Wagner's general technique to prove completeness in the levels of the boolean hierarchy over NP and some related results. In particular, we show that it is DP-complete to decide whether or not a given graph can be colored with ... more >>>

The VP versus VNP question, introduced by Valiant, is probably the most important open question in algebraic complexity theory. Thanks to completeness results, a variant of this question, VBP versus VNP, can be succinctly restated as asking whether the permanent of a generic matrix can be written as a determinant ... more >>>

We provide a list of new natural VNP-intermediate polynomial
families, based on basic (combinatorial) NP-complete problems that
are complete under \emph{parsimonious} reductions. Over finite
fields, these families are in VNP, and under the plausible
hypothesis $\text{Mod}_pP \not\subseteq P/\text{poly}$, are neither VNP-hard (even under
oracle-circuit reductions) nor in VP. Prior to ... more >>>