38 research outputs found
On a Product of Finite Monoids
In this paper, for each positive integer m, we associate with a finite monoid S0 and m finite commutative monoids S1,…, Sm, a product &#x25CAm(Sm,…, S1, S0). We give a representation of the free objects in the pseudovariety &#x25CAm(Wm,…, W1, W0) generated by these (m + 1)-ary products where Si &#x2208 Wi for all 0 &#x2264 i &#x2264 m. We then give, in particular, a criterion to determine when an identity holds in &#x25CAm(J1,…, J1, J1) with the help of a version of the Ehrenfeucht-Fraïssé game (J1 denotes the pseudovariety of all semilattice monoids). The union &#x222Am>0&#x25CAm (J1,…, J1, J1) turns out to be the second level of the Straubing’s dot-depth hierarchy of aperiodic monoids
The omega-inequality problem for concatenation hierarchies of star-free languages
The problem considered in this paper is whether an inequality of omega-terms
is valid in a given level of a concatenation hierarchy of star-free languages.
The main result shows that this problem is decidable for all (integer and half)
levels of the Straubing-Th\'erien hierarchy
Fragments of first-order logic over infinite words
We give topological and algebraic characterizations as well as language
theoretic descriptions of the following subclasses of first-order logic FO[<]
for omega-languages: Sigma_2, FO^2, the intersection of FO^2 and Sigma_2, and
Delta_2 (and by duality Pi_2 and the intersection of FO^2 and Pi_2). These
descriptions extend the respective results for finite words. In particular, we
relate the above fragments to language classes of certain (unambiguous)
polynomials. An immediate consequence is the decidability of the membership
problem of these classes, but this was shown before by Wilke and Bojanczyk and
is therefore not our main focus. The paper is about the interplay of algebraic,
topological, and language theoretic properties.Comment: Conference version presented at 26th International Symposium on
Theoretical Aspects of Computer Science, STACS 200
Fragments of first-order logic over infinite words
We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic for omega-languages: Sigma2, FO2, the intersection of FO2 and Sigma2, and Delta2 (and by duality Pi2 and the intersection of FO2 and Pi2). These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An immediate consequence is the decidability of the membership problem of these classes, but this was shown before by Wilke and Bojanczyk and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties
Logic and Automata
Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field
Recognisable languages over monads
The principle behind algebraic language theory for various kinds of
structures, such as words or trees, is to use a compositional function from the
structures into a finite set. To talk about compositionality, one needs some
way of composing structures into bigger structures. It so happens that category
theory has an abstract concept for this, namely a monad. The goal of this paper
is to propose monads as a unifying framework for discussing existing algebras
and designing new algebras
26. Theorietag Automaten und Formale Sprachen 23. Jahrestagung Logik in der Informatik: Tagungsband
Der Theorietag ist die Jahrestagung der Fachgruppe Automaten und Formale Sprachen der Gesellschaft für Informatik und fand erstmals 1991 in Magdeburg statt. Seit dem Jahr 1996 wird der Theorietag von einem eintägigen Workshop mit eingeladenen Vorträgen begleitet. Die Jahrestagung der Fachgruppe Logik in der Informatik der Gesellschaft für Informatik fand erstmals 1993 in Leipzig statt. Im Laufe beider Jahrestagungen finden auch die jährliche Fachgruppensitzungen statt. In diesem Jahr wird der Theorietag der Fachgruppe Automaten und Formale Sprachen erstmalig zusammen mit der Jahrestagung der Fachgruppe Logik in der Informatik abgehalten. Organisiert wurde die gemeinsame Veranstaltung von der Arbeitsgruppe Zuverlässige Systeme des Instituts für Informatik an der Christian-Albrechts-Universität Kiel vom 4. bis 7. Oktober im Tagungshotel Tannenfelde bei Neumünster. Während des Tre↵ens wird ein Workshop für alle Interessierten statt finden. In Tannenfelde werden • Christoph Löding (Aachen) • Tomás Masopust (Dresden) • Henning Schnoor (Kiel) • Nicole Schweikardt (Berlin) • Georg Zetzsche (Paris) eingeladene Vorträge zu ihrer aktuellen Arbeit halten. Darüber hinaus werden 26 Vorträge von Teilnehmern und Teilnehmerinnen gehalten, 17 auf dem Theorietag Automaten und formale Sprachen und neun auf der Jahrestagung Logik in der Informatik. Der vorliegende Band enthält Kurzfassungen aller Beiträge. Wir danken der Gesellschaft für Informatik, der Christian-Albrechts-Universität zu Kiel und dem Tagungshotel Tannenfelde für die Unterstützung dieses Theorietags. Ein besonderer Dank geht an das Organisationsteam: Maike Bradler, Philipp Sieweck, Joel Day. Kiel, Oktober 2016 Florin Manea, Dirk Nowotka und Thomas Wilk