Theodor Lettmann

Projections of Vector addition system reachability sets are semilinear

Abstract The reachability sets of Vector Addition Systems of dimension six or more can be non-semilinear. This may be one reason why the inclusion problem (as well as the equality problem) for reachability sets of vector addition systems in general is undecidable, even though the reachability problem itself is known to be decidable. We show that any one-dimensional projection of the reachability set of an arbitrary vector addition system is semilinear, and hence “simple”.

Modeling agents and agent systems

In present agent definitions, we often find different names and definitions for similar concepts. Many works on multiagent systems use abstract and informal descriptions to introduce the topic. Even books on multiagent systems often lack a formal definition or use a selfcontained formalism. Our goal is to present a universal and formal description for agent systems that can be used as a core model with other existing models as special cases. This core model allows clear specification of agent systems and their properties. Design decisions are made explicitly and, by that, become a mean of comparison for different approaches. The proposed definitions for single- and multiagent systems address all basic properties while leaving space for extensions and can thus be used to talk about concepts using a homogeneous notation. The comparisons of our definition to existing models show that the most-cited descriptions can be expressed with our formalism which shows that there is a basic consensus on fundamental properties of agent systems.

Reducing Nondeterminism in Automated Service Composition

Automated service composition has been studied as a subject of state based planning for a decade. A great deal of service composition tasks can only be solved if concrete output values of the services are considered in the composition process. However, the fact that those values are not known before runtime leads to nondeterministic planning problems, which have proven to be notoriously difficult in practical automated service composition applications. Even though this problem is frequently recognized, it has still received remarkably few attention and remains unsolved. This paper shows how nondeterminism in automated service composition can be reduced. We introduce context rules as a means to derive semantic knowledge from output values of services. These rules enable us to replace nondeterministic composition operations by less nondeterministic or even completely deterministic ones. We show the validity of our solutions not only theoretically but also have evaluated them practically through implementation.

Resolution remains hard under equivalence

Abstract The basis of this paper is the observation that for several proof systems for propositional formulas in conjunctive normal form there are families of hard examples for which the shortest proof requires superpolynomially many steps. We will show that – under the assumption NP≠coNP – it is impossible to transform formulas into a logically equivalent formula by adding polynomially many clauses such that it can be decided in polynomial time whether a clause is a consequence of the enlarged formula. This result especially holds for resolution, i.e. for all polynomials p and q there exists a formula Φ∈CNF, such that for each equivalent formula Ψ∈CNF with |Ψ|⩽q(|Φ|) there is a clause π with Φ⊨π for which the shortest resolution proof Ψ ⊢ RES π requires more than p(|Φ|+|π|) resolution steps.

Learning a Representation for Optimizable Formulas

Roughly speaking, a class of formulas K is called optimizable, if there is a class K′, such that for each formula in K there exists a short equivalent formula in K′, where the deduction problem of K′ is solvable in polynomial time. We consider the problem, whether for such classes an optimized representation can be learned using membership, equivalence and clause queries.

Datenstrukturen und Normalformen

Fur viele Anwendungen bietet es sich an, Formeln einer bestimmten syntaktischen Struktur zu betrachten. Grunde fur solche Normalformen konnen zum Beispiel die Ubersichtlichkeit der Darstellung sein und damit verbunden eine relativ leichte Veranderbarkeit solcher Formeln oder die Anwendbarkeit dezidierter Algorithmen fur Fragen der Folgerbarkeit und Widerspruchsfreiheit wie z.B. Resolutionsalgorithmen.

Einführung in die Aussagenlogik

Die Logik hat sich seit ihren Anfangen unter anderem mit der Prazisierung des Begriffs des Beweisens, also des logischen Schliesens beschaftigt. Die heutigen technischen Moglichkeiten haben dazu gefuhrt, das verstarkt Fragen der maschinellen Verarbeitung im Vordergrund stehen. Auf der einen Seite ist daher die Verarbeitung der Logik von Interesse und auf der anderen Seite spielen die Pradikatenlogik und die Aussagenlogik als formale Beschreibungsmittel und als theoretisch fundierte Basis eine immer grosere Rolle in der Informatik. Beispiele fur die Anwendung dieser beiden Aspekte der Logik finden wir etwa in der Software-Verifikation und in der Logik-Programmierung.

Classes of first order formulas under various satisfiability definitions

In this paper we consider some special satisfiability problems of first order logic. We study effects of a unique name assumption and a domain closure assumption on complexity of satisfiability tests for certain classes of formulas interesting in logic programming or relational database theory. It is shown that the last assumption simplifies the satisfiability problem for first order logic. However for classes of formulas with lower complexity of the unrestricted satisfiability problem no general reduction of complexity can be determined.