It was shown some years ago that the computation time for many important
Boolean functions of n arguments on concurrent-read exclusive-write
parallel random-access machines
(CREW PRAMs) of unlimited size is at least f(n) = 0.72 log n.
On the other hand, it ... more >>>

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 >>>

For any Boolean function $f$ let $L(f)$ be its formula size
complexity in the basis $\{\land,\oplus,1\}$. For every $n$ and
every $k\le n/2$, we describe a probabilistic distribution
on formulas in the basis $\{\land,\oplus,1\}$ in some given set of
$n$ variables and of the ... more >>>

A theory, in this context, is a Boolean formula; it is
used to classify instances, or truth assignments. Theories
can model real-world phenomena, and can do so more or less
correctly.
The theory revision, or concept revision, problem is to
correct a given, roughly correct concept.
This problem is ... more >>>

We describe a general method for testing whether a function on n input variables has a concise representation. The approach combines ideas from the junta test of Fischer et al. with ideas from learning theory, and yields property testers that make poly(s/epsilon) queries (independent of n) for Boolean function classes ... more >>>

We give an explicit construction of a pseudorandom generator for read-once formulas whose inputs can be read in arbitrary order. For formulas in $n$ inputs and arbitrary gates of fan-in at most $d = O(n/\log n)$, the pseudorandom generator uses $(1 - \Omega(1))n$ bits of randomness and produces an output ... more >>>

We investigate the complexity of the syntactic isomorphism problem of CNF Boolean Formulas (CSFI): given two CNF Boolean formulas $\varphi(a_{1},\ldots,a_{n})$ and $\varphi(b_{1},\ldots,b_{n})$ decide whether there exists a permutation of clauses, a permutation of literals and a bijection between their variables such that $\varphi(a_{1},\ldots,a_{n})$ and $\varphi(b_{1},\ldots,b_{n})$ become syntactically identical. We first ... more >>>

Understanding the power of negation gates is crucial to bridge the exponential gap between monotone and non-monotone computation. We focus on the model of formulas over the De Morgan basis and consider it in a negation-limited setting.

We prove that every formula that contains $t$ negation gates can be shrunk ... more >>>