Cost Automata, Safe Schemes, and Downward Closures

Higher-order recursion schemes are an expressive formalism used to define languages of possibly infinite ranked trees. They extend regular and context-free grammars, and are equivalent to simply typed ?Y-calculus and collapsible pushdown automata. In this work we prove, under a syntactical constraint called safety, decidability of the model-checking problem for recursion schemes against properties defined by alternating B-automata, an extension of alternating parity automata for infinite trees with a boundedness acceptance condition. We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes

Cost Automata, Safe Schemes, and Downward Closures

Higher-order recursion schemes are an expressive formalism used to define languages of possibly infinite ranked trees. They extend regular and context-free grammars, and are equivalent to simply typed $\lambda Y$-calculus and collapsible pushdown automata. In this work we prove, under a syntactical constraint called safety, decidability of the model-checking problem for recursion schemes against properties defined by alternating B-automata, an extension of alternating parity automata for infinite trees with a boundedness acceptance condition. We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes.Comment: accepted at ICALP'2

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

Existential Definability over the Subword Ordering

We study first-order logic (FO) over the structure consisting of finite words over some alphabet A, together with the (non-contiguous) subword ordering. In terms of decidability of quantifier alternation fragments, this logic is well-understood: If every word is available as a constant, then even the ?? (i.e., existential) fragment is undecidable, already for binary alphabets A. However, up to now, little is known about the expressiveness of the quantifier alternation fragments: For example, the undecidability proof for the existential fragment relies on Diophantine equations and only shows that recursively enumerable languages over a singleton alphabet (and some auxiliary predicates) are definable. We show that if |A| ? 3, then a relation is definable in the existential fragment over A with constants if and only if it is recursively enumerable. This implies characterizations for all fragments ?_i: If |A| ? 3, then a relation is definable in ?_i if and only if it belongs to the i-th level of the arithmetical hierarchy. In addition, our result yields an analogous complete description of the ?_i-fragments for i ? 2 of the pure logic, where the words of A^* are not available as constants

Unboundedness Problems for Machines with Reversal-Bounded Counters

We consider a general class of decision problems concerning formal languages, called (one-dimensional) unboundedness predicates, for automata that feature reversal-bounded counters (RBCA). We show that each problem in this class reduces-non-deterministically in polynomial time to the same problem for just nite automata. We also show an analogous reduction for automata that have access to both a push- down stack and reversal-bounded counters (PRBCA). This allows us to answer several open questions: For example, we settle the complexity of deciding whether a given (P)RBCA language L is bounded, meaning whether there exist words w1, . . . , wn with L ⊆ w1∗ · · · wn∗ . For PRBCA, even decidability was open. Our methods also show that there is no language of a (P)RBCA of intermediate growth. Part of our proof is likely of independent interest: We show that one can translate an RBCA into a machine with Z-counters in logarithmic space

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Automata for branching and layered temporal structures: An investigation into regularities of infinite transition systems

This manuscript is a revised version of the PhD Thesis I wrote under the supervision of Prof. Angelo Montanari at Udine University. The leitmotif underlying the results herein provided is that, given any infinite complex system (e.g., a computer program) to be verified against a finite set of properties, there often exists a simpler system that satisfies the same properties and, in addition, presents strong regularities (e.g., periodicity) in its structure. Those regularities can then be exploited to decide, in an effective way, which property is satisfied by the system and which is not. Perhaps the most natural and effective way to deal with inherent regularities of infinite systems is through the notion of finite-state automaton. Intuitively, a finite-state automaton is an abstract machine with only a bounded amount of memory at its disposal, which processes an input (e.g., a sequence of symbols) and eventually outputs true or false, depending on the way the machine was designed and on the input itself. The present book focuses precisely on automaton-based approaches that ease the representation of and the reasoning on properties of infinite complex systems. The most simple notion of finite-state automaton, is that of single-string automaton. Such a device outputs true on a single (finite or infinite) sequence of symbols and false on any other sequence. We will show how single-string automata processing infinite sequences of symbols can be successfully applied in various frameworks for temporal representation and reasoning. In particular, we will use them to model single ultimately periodic time granularities, namely, temporal structures that are left-bounded and that, ultimately, periodically group instants of the underlying temporal domain (a simple example of such a structure is given by the partitioning of the temporal domain of days into weeks). The notion of single-string automaton can be further refined by introducing counters in order to compactly represent repeated occurrences of the same subsequence in the given input. By introducing restricted policies of counter update and by exploiting suitable abstractions of the configuration space for the resulting class of automata, we will devise efficient algorithms for reasoning on quasi-periodic time granularities (e.g., the partitioning of the temporal domain of days into years). Similar abstractions can be used when reasoning on infinite branching (temporal) structures. In such a case, one has to consider a generalized notion of automaton, which is able to process labeled branching structures (hereafter called trees), rather than linear sequences of symbols. We will show that sets of trees featuring the same properties can be identified with the equivalence classes induced by a suitable automaton. More precisely, given a property to be verified, one can first define a corresponding automaton that accepts all and only the trees satisfying that property, then introduce a suitable equivalence relation that refines the standard language equivalence and groups all trees being indistinguishable by the automaton, and, finally, exploit such an equivalence to reduce several instances of the verification problem to equivalent simpler instances, which can be eventually decided