A Rice-style theorem for parallel automata

AbstractWe present a general result, similar to Rice’s theorem, concerning the complexity of detecting properties on finite automata enriched by bounded cooperative concurrency, such as statecharts and abstract parallel automata, which we denote by CFAs (Concurrent Finite Automata). On one extreme, the complexity of detecting non-trivial properties that preserve equivalence of machines, i.e. properties of the accepted language, on finite automata, can be as little as O(1). On the other extreme, Rice’s theorem states that all such properties on Turing machines are undecidable. We state that all the non-trivial properties of the regular (or ω-regular) languages, are PSPACE-hard on CFAs with ϵ-moves and on CFAs without ϵ-moves accepting infinite words. We also extend this result to CFAs without ϵ-moves accepting finite words that satisfy a condition that holds for many properties

Mixing Probabilistic and non-Probabilistic Objectives in Markov Decision Processes

In this paper, we consider algorithms to decide the existence of strategies in MDPs for Boolean combinations of objectives. These objectives are omega-regular properties that need to be enforced either surely, almost surely, existentially, or with non-zero probability. In this setting, relevant strategies are randomized infinite memory strategies: both infinite memory and randomization may be needed to play optimally. We provide algorithms to solve the general case of Boolean combinations and we also investigate relevant subcases. We further report on complexity bounds for these problems.Comment: Paper accepted to LICS 2020 - Full versio

Proceedings of SUMo and CompoNet 2011

International audienc

Synthesis from multi-paradigm specifications

This work proposes a language for describing reactive synthesis problems that integrates imperative and declarative elements. The semantics is defined in terms of two-player turn-based infinite games with full information. Currently, synthesis tools accept linear temporal logic (LTL) as input, but this description is less structured and does not facilitate the expression of sequential constraints. This motivates the use of a structured programming language to specify synthesis problems. Transition systems and guarded commands serve as imperative constructs, expressed in a syntax based on that of the modeling language Promela. The syntax allows defining which player controls data and control flow, and separating a program into assumptions and guarantees. These notions are necessary for input to game solvers. The integration of imperative and declarative paradigms allows using the paradigm that is most appropriate for expressing each requirement. The declarative part is expressed in the LTL fragment of generalized reactivity(1), which admits efficient synthesis algorithms. The implementation translates Promela to input for the Slugs synthesizer and is written in Python

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

Synthesizing Permissive Winning Strategy Templates for Parity Games

We present a novel method to compute \emph{permissive winning strategies} in two-player games over finite graphs with $\omega$-regular winning conditions. Given a game graph $G$ and a parity winning condition $\Phi$, we compute a \emph{winning strategy template} $\Psi$ that collects an infinite number of winning strategies for objective $\Phi$ in a concise data structure. We use this new representation of sets of winning strategies to tackle two problems arising from applications of two-player games in the context of cyber-physical system design -- (i) \emph{incremental synthesis}, i.e., adapting strategies to newly arriving, \emph{additional} $\omega$-regular objectives $\Phi'$, and (ii) \emph{fault-tolerant control}, i.e., adapting strategies to the occasional or persistent unavailability of actuators. The main features of our strategy templates -- which we utilize for solving these challenges -- are their easy computability, adaptability, and compositionality. For \emph{incremental synthesis}, we empirically show on a large set of benchmarks that our technique vastly outperforms existing approaches if the number of added specifications increases. While our method is not complete, our prototype implementation returns the full winning region in all 1400 benchmark instances, i.e., handling a large problem class efficiently in practice.Comment: CAV'2

Formal Specification and Verification for Automated Production Systems

Complex industrial control software often drives safety- and mission-critical systems, like automated production plants or control units embedded into devices in automotive systems. Such controllers have in common that they are reactive systems, i.e., that they periodically read sensor stimuli and cyclically execute the same program to produce actuator signals. The correctness of software for automated production is rarely verified using formal techniques. Although, due to the Industrial Revolution 4.0 (IR4.0), the impact and importance of software have become an important role in industrial automation. What is used instead in industrial practice today is testing and simulation, where individual test cases are used to validate an automated production system. Three reasons why formal methods are not popular are: (a) It is difficult to adequately formulate the desired temporal properties. (b) There is a lack of specification languages for reactive systems that are both sufficiently expressive and comprehensible for practitioners. (c) Due to the lack of an environment model the obtained results are imprecise. Nonetheless, formal methods for automated production systems are well studied academically---mainly on the verification of safety properties via model checking. In this doctoral thesis we present the concept of (1) generalized test tables (GTTs), a new specification language for functional properties, and their extension (2) relational test tables (RTTs) for relational properties. The concept includes the syntactical notion, designed for the intuition of engineers, and the semantics, which are based on game theory. We use RTTs for a novel confidential property on reactive systems, the provably forgetting of information. Moreover, for regression verification, an important relational property, we are able to achieve performance improvements by (3) creating a decomposing rule which splits large proofs into small sub-task. We implemented the verification procedures and evaluated them against realistic case studies, e.g., the Pick-and-Place-Unit from the Technical University of Munich. The presented contribution follows the idea of lowering the obstacle of verifying the dependability of reactive systems in general, and automated production systems in particular for the engineer either by introducing a new specification language (GTTs), by exploiting existing programs for the specification (RTTs, regression verification), or by improving the verification performance

Automata and linear temporal logic : translations with transition-based acceptance

Automata theory provides powerful tools for designing and implementing decision procedures for temporal logics and their applications to the automatic verification of systems against their logical specifications. Implementing these decision procedures by making use of automata built from the systems and their specifications with translation procedures is challenging in practice due to the tendency of the automata to grow easily unmanageably large as the size of the systems or the logical specifications increases. This thesis develops the theory of translating propositional linear time temporal logic (LTL) into nondeterministic automata via self-loop alternating automata. Unlike nondeterministic automata, self-loop alternating automata are expressively equivalent to LTL and allow a conceptually simple translation of LTL specifications into automata using a set of rules for building automata incrementally from smaller components. The use of generalized transition-based acceptance for automata throughout all constructions gives rise to new optimized translation rules and facilitates designing heuristics for the minimization of automata by making use of language containment tests combined with structural analysis of automata. The generalized definition also supports the translation of self-loop alternating automata into nondeterministic automata by essentially applying the standard subset construction; this construction can be further simplified and optimized when working with automata built from LTL formulas. The translation rules can also be used to identify a syntactic subclass of LTL for which the exponential increase caused by the subset construction in the number of states of the automaton can always be avoided; consequently, the satisfiability problem for this subclass, which is shown to extend related subclasses known from the literature, is NP-complete. Additionally, the emptiness of generalized nondeterministic automata is shown to be testable without giving up generalized transition-based acceptance by using a new variant of the well-known nested depth-first search algorithm with improved worst-case resource requirements.Automaattiteorian avulla voidaan suunnitella ja toteuttaa temporaalilogiikkojen ratkaisumenetelmiä sekä näiden menetelmien sovellutuksia logiikoilla järjestelmistä esitettyjen oikeellisuusvaatimusten tietokoneavusteiseen verifiointiin. Käytännössä näiden ratkaisumenetelmien toteuttaminen kääntämällä järjestelmät ja niiden oikeellisuusvaatimukset automaateiksi on kuitenkin haasteellista, sillä näistä automaateista tulee järjestelmien tai loogisten vaatimusten koon kasvaessa helposti niin suuria, ettei niitä enää voida käsitellä. Tässä väitöskirjassa kehitetään lineaarisen ajan temporaalilogiikan (LTL) epädeterministisiksi automaateiksi kääntämisen teoriaa käyttämällä käännöksen apuna vain yhden tilan silmukoita sisältäviä alternoivia automaatteja, joilla – toisin kuin epädeterministisillä automaateilla – on sama ilmaisuvoima kuin lineaarisen ajan temporaalilogiikalla. Tätä logiikkaa voidaan kääntää näiksi automaateiksi soveltaen yksinkertaisia sääntöjä automaattien yhdistämiseksi vaiheittain keskenään yhä suuremmiksi automaateiksi. Käyttämällä yleistettyä siirtymäpohjaista hyväksyvyyden määritelmää automaateille kaikissa käännöksen vaiheissa voidaan näin muodostettuja automaatteja sieventää uusin tavoin käyttäen apuna automaattien hyväksymien kielten välisiä sisältyvyyssuhteita sekä automaattien rakenteellisia ominaisuuksia. Yleistetyn määritelmän ansiosta vain yhden tilan silmukoita sisältävät alternoivat automaatit voidaan myös kääntää edelleen epädeterministisiksi automaateiksi soveltamalla yleisesti tunnettua osajoukkokonstruktiota lähes sellaisenaan. Tämä konstruktio voidaan edelleen tehdä yksinkertaisemmin ja tehokkaammin LTL-kaavoista muodostetuille automaateille. Automaattikäännöksessä käytettävien sääntöjen avulla voidaan myös erottaa lineaarisen ajan temporaalilogiikan syntaktinen osajoukko, jonka kaavat onmahdollista kääntää epädeterministisiksi automaateiksi ilman, että automaattien tilojen määrä kasvaa osajoukkokonstruktion tavoin eksponentiaalisesti. Tästä tuloksesta seuraa, että kyseisen LTL:n osajoukon toteutuvuusongelma on NP-täydellinen. Osajoukko on samankaltaisia kirjallisuudessa aiemmin esiteltyjä osajoukkoja aidosti laajempi. Väitöskirjassa esitetään myös, kuinka epädeterministisen automaatin hyväksymän kielen tyhjyys voidaan tarkastaa luopumatta yleistetystä siirtymäpohjaisesta hyväksyvyyden määritelmästä käyttäen algoritmia, joka on uusi, huonoimman tapauksen vaatimuksiltaan tehokkaampi muunnos tunnetusta sisäkkäisestä syvyyshakualgoritmista.reviewe