Multi-Head Finite Automata: Characterizations, Concepts and Open Problems

Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even non-semi-decidable problems on these devices such as, for example, emptiness, finiteness, universality, equivalence, etc. These strong negative results trigger the study of subclasses and alternative characterizations of multi-head finite automata for a better understanding of the nature of non-recursive trade-offs and, thus, the borderline between decidable and undecidable problems. In the present paper, we tour a fragment of this literature

Equivalence of infinite-state systems with silent steps

This dissertation contributes to analysis methods for infinite-state systems. The dissertation focuses on equivalence testing for two relevant classes of infinite-state systems: commutative context-free processes, and one-counter automata. As for equivalence notions, we investigate the classical bisimulation and simulation equivalences. The important point is that we allow for silent steps in the model, abstracting away from internal, unobservable actions. Very few decidability results have been known so far for bisimulation or simulation equivalence for infinite-state systems with silent steps, as presence of silent steps makes the equivalence problem arguably harder to solve. A standard technique for bisimulation or simulation equivalence testing is to use the hierarchy of approximants. For an effective decision procedure the hierarchy must stabilize (converge) at level omega, the first limit ordinal, which is not the case for the models investigated in this thesis. However, according to a long-standing conjecture, the community believed that the convergence actually takes place at level omega+ omega in the class of commutative context free processes. We disprove the conjecture and provide a lower bound of omega * omega for the convergence level. We also show that all previously known positive decidability results for BPPs can be re-proven uniformly using the improved approximants techniques. Moreover dissertation contains an unsuccesfull attack on one of the main open problems in the area: decidability of weak bisimulation equivalence for commutative context-free processes. Our technical development of this section is not sufficient to solve the problem, but we believe it is a serious step towards a solution. Furtermore, we are able to show decidability of branching (stuttering) bisimulation equivalence, a slightly more discriminating variant of bisimulation equivalence. It is worth emphesizing that, until today, our result is the only known decidability result for bisimulation equivalence in a class of inifinite-state systems with silent steps that is not known to admit convergence of (some variant of) standard approximants at level omega. Finally we consider weak simulation equivalence over one-counter automata without zero tests (allowing zero tests implies undecidability). While weak bisimulation equivalence is known to be undecidable in this class, we prove a surprising result that weak simulation equivalence is actually decidable. Thus we provide a first example going against a trend, widely-believed by the community, that simulation equivalence tends to be computationally harder than bisimulation equivalence. In short words, the dissertation contains three new results, each of them solving a non-trivial open problem about equivalence testing of infinite-state systems with silent steps

Convex Hull of Arithmetic Automata

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata

Polynomial Learnability of Semilinear Sets

We characterize learnability and non-learnability of subsets of Nm called \u27semilinear sets\u27, with respect to the distribution-free learning model of Valiant. In formal language terms, semilinear sets are exactly the class of \u27letter-counts\u27 (or Parikh-images) of regular sets. We show that the class of semilinear sets of dimensions 1 and 2 is learnable, when the integers are encoded in unary. We complement this result with negative results of several different sorts, relying on hardness assumptions of varying degrees - from P ≠ NP and RP ≠ NP to the hardness of learning DNF. We show that the minimal consistent concept problem is NP-complete for this class, verifying the non-triviality of our learnability result. We also show that with respect to the binary encoding of integers, the corresponding \u27prediction\u27 problem is already as hard as that of DNF, for a class of subsets of Nm much simpler than semilinear sets. The present work represents an interesting class of countably infinite concepts for which the questions of learnability have been nearly completely characterized. In doing so, we demonstrate how various proof techniques developed by Pitt and Valiant [14], Blumer et al. [3], and Pitt and Warmuth [16] can be fruitfully applied in the context of formal languages

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