Parity and generalised Büchi automata - determinisation and complementation

In this thesis, we study the problems of determinisation and complementation of finite automata on infinite words. We focus on two classes of automata that occur naturally: generalised Büchi automata and nondeterministic parity automata. Generalised Büchi and parity automata occur naturally in model-checking, realisability checking and synthesis procedures. We first review a tight determinisation procedure for Büchi automata, which uses a simplification of Safra trees called history trees. As Büchi automata are special types of both generalised Büchi and parity automata, we adjust the data structure to arrive at suitably tight determinisation constructions for both generalised Büchi and parity automata. As the parity condition describes combinations of Büchi and CoBüchi conditions, instead of immediately modifying the data structure to handle parity automata, we arrive at a suitable data structure by first looking at a special case, Rabin automata with one accepting pair. One pair Rabin automata correspond to parity automata with three priorities and serve as a starting point to modify the structures that result from Büchi determinisation: we then nest these structures to reflect the standard parity condition and describe a direct determinisation construction. The generalised Büchi condition is characterised by an accepting family with 'k' accepting sets. It is easy to extend classic determinisation constructions to handle generalised Büchi automata by incorporating the degeneralization algorithm in the determinisation construction. We extend the tight Büchi construction to do exactly this. Our determinisation constructions go to deterministic Rabin automata. It is known that one can determinise to the more convenient parity condition by incorporating the standard Latest Appearance Record construction in the determinisation procedure. We determinise to parity automata using this technique. We prove lower bounds on these constructions. In the case of determinisation to Rabin automata, our constructions are tight to the state. In the case of determinisation to parity, there is a constant factor ≤ 1.5 between upper and lower bounds reducing to optimal(to the state) in the case of Büchi and 1-pair Rabin. We also reconnect tight determinisation and complementation and provide constructions for complementing generalised Büchi and parity automata by starting withour data structure for determinisation. We introduce suitable data structures for the complementation procedures based on the data structure used for determinisation. We prove lower bounds for both constructions that are tight upto an O(n) factor where 'n' is the number of states of the nondeterministic automaton that is complemented

Determinization of B\"uchi Automata: Unifying the Approaches of Safra and Muller-Schupp

Determinization of B\"uchi automata is a long-known difficult problem and after the seminal result of Safra, who developed the first asymptotically optimal construction from B\"uchi into Rabin automata, much work went into improving, simplifying or avoiding Safra's construction. A different, less known determinization construction was derived by Muller and Schupp and appears to be unrelated to Safra's construction on the first sight. In this paper we propose a new meta-construction from nondeterministic B\"uchi to deterministic parity automata which strictly subsumes both the construction of Safra and the construction of Muller and Schupp. It is based on a correspondence between structures that are encoded in the macrostates of the determinization procedures - Safra trees on one hand, and levels of the split-tree, which underlies the Muller and Schupp construction, on the other. Our construction allows for combining the mentioned constructions and opens up new directions for the development of heuristics.Comment: Full version of ICALP 2019 pape

Propositional Dynamic Logic for Hyperproperties

Information security properties of reactive systems like non-interference often require relating different executions of the system to each other and following them simultaneously. Such hyperproperties can also be useful in other contexts, e.g., when analysing properties of distributed systems like linearizability. Since common logics like LTL, CTL, or the modal ?-calculus cannot express hyperproperties, the hyperlogics HyperLTL and HyperCTL^* were developed to cure this defect. However, these logics are not able to express arbitrary ?-regular properties. In this paper, we introduce HyperPDL-?, an adaptation of the Propositional Dynamic Logic of Fischer and Ladner for hyperproperties, in order to remove this limitation. Using an elegant automata-theoretic framework, we show that HyperPDL-? model checking is asymptotically not more expensive than HyperCTL^* model checking, despite its vastly increased expressive power. We further investigate fragments of HyperPDL-? with regard to satisfiability checking

Complementing Büchi automata with a subset-tuple construction

Complementation of Büchi automata is well known for being difficult. In the worst case, a state-space growth of (0:76n)n is unavoidable. Recent studies suggest that “simpler” algorithms perform better than more involved ones on practical cases. In this paper, we present a simple “direct” algorithm for complementing Büchi automata. It involves a structured subset construction (using tuples of subsets of states) that produces a deterministic automaton. This construction leads to a complementation procedure that resembles the straightforward complementation algorithm for deterministic Büchi automata, the latter algorithm actually being a special case of our construction

Index appearance record with preorders

Transforming ω-automata into parity automata is traditionally done using appearance records. We present an efficient variant of this idea, tailored to Rabin automata, and several optimizations applicable to all appearance records. We compare the methods experimentally and show that our method produces significantly smaller automata than previous approaches

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

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems