Some Undecidability Results related to the Star Problem in Trace Monoids

This paper deals with decision problems related to the star problem in trace monoids, which means to determine whether the iteration of a recognizable trace language is recognizable. Due to a theorem by Richomme from 1994[30,31], we know that the Star Problem is decidable in trace monoids which do not contain a C4-submonoid. The C4 is (isomorphic to) the Caresian Product of two free monoids over doubleton alphabets. It is not known, whether the Star Problem is decidable in C4 or in trace monoids containing a C4. In this paper, we show undecidability of some related problems: Assume a trace monoid which contains a C4. Then, it is undecidable whether for two given recognizable languages K and L, we have K ⊆ L*, although we can decide K* ⊆ L. Further, we can not decide recognizability of K ∩ L* as well as universality and recognizability of K U L*

Two Techniques in the Area of the Star Problem

This paper deals with decision problems related to the star problem in trace monoids, which means to determine whether the iteration of a recognizable trace language is recognizable. Due to a theorem by G. Richomme from 1994 [32, 33], we know that the star problem is decidable in trace monoids which do not contain a submonoid of the form {a,c}* x {b,d}*. Here, we consider a more general problem: Is it decidable whether for some recognizable trace language and some recognizable or finite trace language P the intersection R ∩ P* is recognizable? If P is recognizable, then we show that this problem is decidale iff the underlying trace monoid does not contain a submonoid of the form {a,c}* x b*. In the case of finite languages P, we show several decidability and undecidability results

Automata and rational expressions

This text is an extended version of the chapter 'Automata and rational expressions' in the AutoMathA Handbook that will appear soon, published by the European Science Foundation and edited by JeanEricPin

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

A counterexample to Thiagarajan's conjecture on regular event structures

We provide a counterexample to a conjecture by Thiagarajan (1996 and 2002) that regular event structures correspond exactly to event structures obtained as unfoldings of finite 1-safe Petri nets. The same counterexample is used to disprove a closely related conjecture by Badouel, Darondeau, and Raoult (1999) that domains of regular event structures with bounded $\natural$-cliques are recognizable by finite trace automata. Event structures, trace automata, and Petri nets are fundamental models in concurrency theory. There exist nice interpretations of these structures as combinatorial and geometric objects. Namely, from a graph theoretical point of view, the domains of prime event structures correspond exactly to median graphs; from a geometric point of view, these domains are in bijection with CAT(0) cube complexes. A necessary condition for both conjectures to be true is that domains of regular event structures (with bounded $\natural$-cliques) admit a regular nice labeling. To disprove these conjectures, we describe a regular event domain (with bounded $\natural$-cliques) that does not admit a regular nice labeling. Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex whose universal cover is a CAT(0) square complex containing a particular plane with an aperiodic tiling. We prove that other counterexamples to Thiagarajan's conjecture arise from aperiodic 4-way deterministic tile sets of Kari and Papasoglu (1999) and Lukkarila (2009). On the positive side, using breakthrough results by Agol (2013) and Haglund and Wise (2008, 2012) from geometric group theory, we prove that Thiagarajan's conjecture is true for regular event structures whose domains occur as principal filters of hyperbolic CAT(0) cube complexes which are universal covers of finite nonpositively curved cube complexes