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 >>>

The class NC$^1$ of problems solvable by bounded fan-in circuit families of logarithmic depth is known to be contained in logarithmic space L, but not much about the converse is known. In this paper we examine the structure of classes in between NC$^1$ and L based on counting functions or, ... more >>>

In a seminal paper from 1985, Sistla and Clarke showed
that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete
or PSPACE-complete, depending on the set of temporal operators used.
If, in contrast, the set of propositional operators is restricted, the complexity may decrease.
... more >>>

We study the complexity of the following algorithmic problem: Given a Boolean function $f$ and a finite set of Boolean functions $B$, decide if there is a circuit with basis $B$ that computes $f$. We show that if both $f$ and all functions in $B$ are given by their truth-table, ... more >>>

In this paper we will look at restricted versions of the evaluation problem, the model checking problem, the equivalence problem, and the counting problem for quantified propositional formulas, both with and without bound on the number of quantifier alternations. The restrictions are such that we consider formulas in conjunctive normal-form ... more >>>

In a seminal paper from 1985, Sistla and Clarke showed
that satisfiability for Linear Temporal Logic (LTL) is either
NP-complete or PSPACE-complete, depending on the set of temporal
operators used

If, in contrast, the set of propositional operators is restricted, the
complexity may ... more >>>

We consider constraint satisfaction problems parameterized by the set of allowed constraint predicates. We examine the complexity of quantified constraint satisfaction problems with a bounded number of quantifier alternations and the complexity of the associated counting problems. We obtain classification results that completely solve the Boolean case, and we show ... more >>>

Schaefer proved in 1978 that the Boolean constraint satisfaction problem for a given constraint language is either in P or is NP-complete, and identified all tractable cases. Schaefer's dichotomy theorem actually shows that there are at most two constraint satisfaction problems, up to polynomial-time isomorphism (and these isomorphism types are ... more >>>

We show that the class of integer-valued functions computable by
polynomial-space Turing machines is exactly the class of functions f
for which there is a nondeterministic polynomial-time Turing
machine with a certain order on its paths that on input x outputs a 3x3
matrix with entries from {-1,0,1} on each ... more >>>

A binary sequence A=A(0)A(1).... is called i.o. Turing-autoreducible if A is reducible to itself via an oracle Turing machine that never queries its oracle at the current input, outputs either A(x) or a don't-know symbol on any given input x, and outputs A(x) for infinitely many x. If in addition ... more >>>

Motivated by the question of how to define an analog of interactive
proofs in the setting of logarithmic time- and space-bounded
computation, we study complexity classes defined in terms of
operators quantifying over oracles. We obtain new
characterizations of $\NCe$, $\L$, $\NL$, $\NP$, ... more >>>

We consider the problems of finding the lexicographically
minimal (or maximal) satisfying assignment of propositional
formulae for different restricted formula classes. It turns
out that for each class from our framework, the above problem
is either polynomial time solvable or complete for ... more >>>

We define and examine several probabilistic operators ranging over sets
(i.e., operators of type 2), among them the formerly studied
ALMOST-operator. We compare their power and prove that they all coincide
for a wide variety of classes. As a consequence, we characterize the
ALMOST-operator which ranges over infinite objects ... more >>>

We show that examinations of the expressive power of logical formulae
enriched by Lindstroem quantifiers over ordered finite structures
have a well-studied complexity-theoretic counterpart: the leaf
language approach to define complexity classes. Model classes of
formulae with Lindstroem quantifiers are nothing else than leaf
language definable sets. Along the ... more >>>