In this paper, we present stronger results in the theory of succinct
problem representation by boolean circuits, and establish a close
relationship between succinct problems and leaf languages. As
a major tool, we use quantifierfree projection reductions
from descriptive complexity theory.

In particular, we show that the succinct upgrading ... more >>>

Building upon the known generalized-quantifier-based first-order
characterization of LOGCFL, we lay the groundwork for a deeper
investigation. Specifically, we examine subclasses of LOGCFL arising
from varying the arity and nesting of groupoidal quantifiers. Our
work extends the elaborate theory relating monoidal quantifiers to
NC^1 and its subclasses. In the ... 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 >>>

We formulate a formal syntax of approximate formulas for the logic with counting
quantifiers, $\mathcal{SOLP}$, studied by us in \cite{aaco06}, where we showed the
following facts:
$(i)$ In the presence of a built--in (linear) order, $\mathcal{SOLP}$ can
describe {\bf NP}--complete problems and fragments of it capture classes like
{\bf P} ... more >>>

In Descriptive Complexity, there is a vast amount of literature on
decision problems, and their classes such as \textbf{P, NP, L and NL}. ~
However, research on the descriptive complexity of optimisation problems
has been limited. In a previous paper [Man], we characterised
the optimisation versions of \textbf{P} via expressions ... more >>>

Model theory is a branch of mathematical logic that investigates the
logical properties of mathematical structures. It has been quite
successfully applied to computational complexity resulting in an
area of research called descriptive complexity theory. Descriptive
complexity is essentially a syntactical characterization of
complexity classes using logical formalisms. However, there ... more >>>

We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic $\mathcal{L}$ we introduce a new logic $\mathsf{BP}\mathcal{L}$, bounded error probabilistic $\mathcal{L}$, which is defined from $\mathcal{L}$ in a similar way as the
complexity class $\mathsf{BPP}$, bounded error probabilistic polynomial time, is defined ... more >>>

Based on different concepts to obtain a finer notion of language recognition via finite monoids we develop an algebraic structure called typed monoid.
This leads to an algebraic description of regular and non regular languages.

We obtain for each language a unique minimal recognizing typed monoid, the typed syntactic monoid.
more >>>

We consider first order logic over words and show FO+MOD[<] is contained in MAJ[<] with three variables.
It is known that for the classes FO[<], FO+MOD[<], FO+GROUP[<] three variables suffice. In the case of MOD[<] even two variables are sufficient.

As a consequence we know that if TC^ 0 neq ... more >>>

Ehrenfeucht-Fraisse games and their generalizations have been quite successful in finite model theory and yield various inexpressibility results. However, for key problems such as P $\ne$ NP or NP $\ne$ coNP no progress has been achieved using the games. We show that for these problems it is already hard to ... more >>>

We prove near-optimal trade-offs for quantifier depth versus number of variables in first-order logic by exhibiting pairs of n-element structures that can be distinguished by a k-variable first-order sentence but where every such sentence requires quantifier depth at least n^?(k/log k). Our trade-offs also apply to first-order counting logic, and ... more >>>