1,114 research outputs found
Approximate automata for omega-regular languages
Automata over infinite words, also known as ω -automata, play a key role in the verification and synthesis of reactive systems. The spectrum of ω -automata is defined by two characteristics: the acceptance condition (e.g. Büchi or parity) and the determinism (e.g., deterministic or nondeterministic) of an automaton. These characteristics play a crucial role in applications of automata theory. For example, certain acceptance conditions can be handled more efficiently than others by dedicated tools and algorithms. Furthermore, some applications, such as synthesis and probabilistic model checking, require that properties are represented as some type of deterministic ω -automata. However, properties cannot always be represented by automata with the desired acceptance condition and determinism.
In this paper we study the problem of approximating linear-time properties by automata in a given class. Our approximation is based on preserving the language up to a user-defined precision given in terms of the size of the finite lasso representation of infinite executions that are preserved. We study the state complexity of different types of approximating automata, and provide constructions for the approximation within different automata classes, for example, for approximating a given automaton by one with a simpler acceptance condition
Model counting for reactive systems
Model counting is the problem of computing the number of solutions for a logical formula. In the last few years, it has been primarily studied for propositional logic, and has been shown to be useful in many applications. In planning, for example, propositional model counting has been used to compute the robustness of a plan in an incomplete domain. In information-flow control, model counting has been applied to measure the amount of information leaked by a security-critical system. In this thesis, we introduce the model counting problem for linear-time properties, and show its applications in formal verification. In the same way propositional model counting generalizes the satisfiability problem for propositional logic, counting models for linear-time properties generalizes the emptiness problem for languages over infinite words to one that asks for the number of words in a language. The model counting problem, thus, provides a foundation for quantitative extensions of model checking, where not only the existence of computations that violate the specification is determined, but also the number of such violations. We solve the model counting problem for the prominent class of omega-regular properties. We present algorithms for solving the problem for different classes of properties, and show the advantages of our algorithms in comparison to indirect approaches based on encodings into propositional logic. We further show how model counting can be used for solving a variety of quantitative problems in formal verification, including probabilistic model checking, quantitative information-flow in security-critical systems, and the synthesis of approximate implementations for reactive systems.Das Modellzählproblem fragt nach der Anzahl der Lösungen einer logischen Formel, und wurde in den letzten Jahren hauptsächlich für Aussagenlogik untersucht. Das Zählen von Modellen aussagenlogischer Formeln hat sich in vielen Anwendungen als nützlich erwiesen. Im Bereich der künstlichen Intelligenz wurde das Zählen von Modellen beispielsweise verwendet, um die Robustheit eines Plans in einem unvollständigen Weltmodell zu bewerten. Das Zählen von Modellen kann auch verwendet werden, um in sicherheitskritischen Systemen die Menge an enthüllten vertraulichen Daten zu messen. Diese Dissertation stellt das Modellzählproblem für Linearzeiteigenschaften vor, und untersucht dessen Rolle in der Welt der formalen Verifikation. Das Zählen von Modellen für Linearzeiteigenschaften führt zu neuen quantitativen Erweiterungen klassischer Verifikationsprobleme, bei denen nicht nur die Existenz eines Fehlers in einem System zu überprüfen ist, sondern auch die Anzahl solcher Fehler. Wir präsentieren Algorithmen zur Lösung des Modellzählproblems für verschiedene Klassen von Linearzeiteigenschaften und zeigen die Vorteile unserer Algorithmen im Vergleich zu indirekten Ansätzen, die auf Kodierungen der untersuchten Probleme in Aussagenlogik basieren. Darüberhinaus zeigen wir wie das Zählen von Modellen zur Lösung einer Vielzahl quantitativer Probleme in der formalen Verifikation verwendet werden kann. Dies beinhaltet unter anderem die Analyse probabilistischer Modelle, die Kontrolle quantitativen Informationsflusses in sicherheitskritischen Systemen, und die Synthese von approximativen Implementierungen für reaktive Systeme
Enhancing Approximations for Regular Reachability Analysis
This paper introduces two mechanisms for computing over-approximations of
sets of reachable states, with the aim of ensuring termination of state-space
exploration. The first mechanism consists in over-approximating the automata
representing reachable sets by merging some of their states with respect to
simple syntactic criteria, or a combination of such criteria. The second
approximation mechanism consists in manipulating an auxiliary automaton when
applying a transducer representing the transition relation to an automaton
encoding the initial states. In addition, for the second mechanism we propose a
new approach to refine the approximations depending on a property of interest.
The proposals are evaluated on examples of mutual exclusion protocols
Kleene Algebras and Semimodules for Energy Problems
With the purpose of unifying a number of approaches to energy problems found
in the literature, we introduce generalized energy automata. These are finite
automata whose edges are labeled with energy functions that define how energy
levels evolve during transitions. Uncovering a close connection between energy
problems and reachability and B\"uchi acceptance for semiring-weighted
automata, we show that these generalized energy problems are decidable. We also
provide complexity results for important special cases
Learn with SAT to Minimize B\"uchi Automata
We describe a minimization procedure for nondeterministic B\"uchi automata
(NBA). For an automaton A another automaton A_min with the minimal number of
states is learned with the help of a SAT-solver.
This is done by successively computing automata A' that approximate A in the
sense that they accept a given finite set of positive examples and reject a
given finite set of negative examples. In the course of the procedure these
example sets are successively increased. Thus, our method can be seen as an
instance of a generic learning algorithm based on a "minimally adequate
teacher" in the sense of Angluin.
We use a SAT solver to find an NBA for given sets of positive and negative
examples. We use complementation via construction of deterministic parity
automata to check candidates computed in this manner for equivalence with A.
Failure of equivalence yields new positive or negative examples. Our method
proved successful on complete samplings of small automata and of quite some
examples of bigger automata.
We successfully ran the minimization on over ten thousand automata with
mostly up to ten states, including the complements of all possible automata
with two states and alphabet size three and discuss results and runtimes;
single examples had over 100 states.Comment: In Proceedings GandALF 2012, arXiv:1210.202
Non-Zero Sum Games for Reactive Synthesis
In this invited contribution, we summarize new solution concepts useful for
the synthesis of reactive systems that we have introduced in several recent
publications. These solution concepts are developed in the context of non-zero
sum games played on graphs. They are part of the contributions obtained in the
inVEST project funded by the European Research Council.Comment: LATA'16 invited pape
Tree games with regular objectives
We study tree games developed recently by Matteo Mio as a game interpretation
of the probabilistic -calculus. With expressive power comes complexity.
Mio showed that tree games are able to encode Blackwell games and,
consequently, are not determined under deterministic strategies.
We show that non-stochastic tree games with objectives recognisable by
so-called game automata are determined under deterministic, finite memory
strategies. Moreover, we give an elementary algorithmic procedure which, for an
arbitrary regular language L and a finite non-stochastic tree game with a
winning objective L decides if the game is determined under deterministic
strategies.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Omega-Regular Reward Machines
Reinforcement learning (RL) is a powerful approach for training agents to
perform tasks, but designing an appropriate reward mechanism is critical to its
success. However, in many cases, the complexity of the learning objectives goes
beyond the capabilities of the Markovian assumption, necessitating a more
sophisticated reward mechanism. Reward machines and omega-regular languages are
two formalisms used to express non-Markovian rewards for quantitative and
qualitative objectives, respectively. This paper introduces omega-regular
reward machines, which integrate reward machines with omega-regular languages
to enable an expressive and effective reward mechanism for RL. We present a
model-free RL algorithm to compute epsilon-optimal strategies against
omega-egular reward machines and evaluate the effectiveness of the proposed
algorithm through experiments.Comment: To appear in ECAI-202
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