We attempt to reconcile the two distinct views of approximation
classes: syntactic and computational.
Syntactic classes such as MAX SNP allow for clean complexity-theoretic
results and natural complete problems, while computational classes such
as APX allow us to work with problems whose approximability is
well-understood. Our results give a computational ... more >>>

We provide a compendium of problems that are complete for
symmetric logarithmic space (SL). Complete problems are one method
of studying this class for which programming is nonintuitive. A
number of the problems in the list were not previously known to be
complete. A ... more >>>

In this paper we study the approximability of boolean constraint
satisfaction problems. A problem in this class consists of some
collection of ``constraints'' (i.e., functions
$f:\{0,1\}^k \rightarrow \{0,1\}$); an instance of a problem is a set
of constraints applied to specified subsets of $n$ boolean
variables. Schaefer earlier ... more >>>

This paper continues the work initiated by Creignou [Cre95] and
Khanna, Sudan and Williamson [KSW96] who classify maximization
problems derived from boolean constraint satisfaction. Here we
study the approximability of {\em minimization} problems derived
thence. A problem in this framework is characterized by a
collection F ... more >>>

We present the first complete problem for SZK, the class of (promise)
problems possessing statistical zero-knowledge proofs (against an
honest verifier). The problem, called STATISTICAL DIFFERENCE, is to
decide whether two efficiently samplable distributions are either
statistically close or far apart. This gives a new characterization
of SZK that makes ... more >>>

Deciding whether a vertex in a graph is reachable from another
vertex has been studied intensively in complexity theory and is
well understood. For common types of graphs like directed graphs,
undirected graphs, dags or trees it takes a (possibly
nondeterministic) logspace machine to decide the reachability
problem, and ... more >>>

The notion of promise problems was introduced and initially studied
by Even, Selman and Yacobi
(Information and Control, Vol.~61, pages 159-173, 1984).
In this article we survey some of the applications that this
notion has found in the twenty years that elapsed.
These include the notion ... more >>>

We introduce some operators defining new complexity classes from existing ones in the Blum-Shub-Smale theory of computation over the reals. Each one of these operators is defined with the help of a quantifier differing from the usual ones, $\forall$ and $\exists$, and yet having a precise geometric meaning. Our agenda ... more >>>

We present a cryptosystem which is complete for the class of probabilistic public-key cryptosystems with bounded error. Besides traditional encryption schemes such as RSA and El Gamal, this class contains probabilistic encryption of Goldwasser-Micali as well as Ajtai-Dwork and NTRU cryptosystems. The latter two are known to make errors with ... more >>>

We study class AvgBPP that consists of distributional problems that can be solved in average polynomial time (in terms of Levin's average-case complexity) by randomized algorithms with bounded error. We prove that there exists a distributional problem that is complete for AvgBPP under polynomial-time samplable distributions. Since we use deterministic ... more >>>

Approximating the eigenvalues of a Hermitian operator can be solved
by a quantum logspace algorithm. We introduce the problem of
approximating the eigenvalues of a given matrix in the context of
classical space-bounded computation. We show that:

- Approximating the second eigenvalue of stochastic operators (in a
certain range of ... more >>>