We provide <i>unconditional</i> constructions of <i>concurrent</i>
statistical zero-knowledge proofs for a variety of non-trivial
problems (not known to have probabilistic polynomial-time
algorithms). The problems include Graph Isomorphism, Graph
Nonisomorphism, Quadratic Residuosity, Quadratic Nonresiduosity, a
restricted version of Statistical Difference, and approximate
versions of the (<b>coNP</b> forms of the) Shortest Vector ... more >>>

We introduce a "derandomized" analogue of graph squaring. This
operation increases the connectivity of the graph (as measured by the
second eigenvalue) almost as well as squaring the graph does, yet only
increases the degree of the graph by a constant factor, instead of
squaring the degree.

One application of ... more >>>

We study counting various types of con gurations in certain classes of graph
automata viewed as discrete dynamical systems. The graph automata models
of our interest are Sequential and Synchronous Dynamical Systems (SDSs and
SyDSs, respectively). These models have been proposed as a mathematical foun-
dation for a theory of ... more >>>