Book•
Automata logics, and infinite games: a guide to current research
01 Jan 2002-
TL;DR: The 19 chapters presented in this multi-author monograph give a consolidated overview of the research results achieved in the theory of automata, logics, and infinite games during the past 10 years.
Abstract: A central aim and ever-lasting dream of computer science is to put the development of hardware and software systems on a mathematical basis which is both firm and practical. Such a scientific foundation is needed especially for the construction of reactive programs, like communication protocols or control systems.
For the construction and analysis of reactive systems an elegant and powerful theory has been developed based on automata theory, logical systems for the specification of nonterminating behavior, and infinite two-person games.
The 19 chapters presented in this multi-author monograph give a consolidated overview of the research results achieved in the theory of automata, logics, and infinite games during the past 10 years. Special emphasis is placed on coherent style, complete coverage of all relevant topics, motivation, examples, justification of constructions, and exercises.
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23 Jul 2012TL;DR: The author not only provides a thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and the extension of formal language theory to finite graphs.
Abstract: The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The author not only provides a thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
479 citations
TL;DR: This paper addresses closure properties under the Boolean operators union, intersection and complementation and algorithmic aspects, such as checking emptiness or language containment, and provides a comparison of probabilistic ω-automata concerning expressiveness and efficiency.
Abstract: Probabilistic ω-automata are variants of nondeterministic automata over infinite words where all choices are resolved by probabilistic distributions Acceptance of a run for an infinite input word can be defined using traditional acceptance criteria for ω-automata, such as Buchi, Rabin or Streett conditions The accepted language of a probabilistic ω-automata is then defined by imposing a constraint on the probability measure of the accepting runs In this paper, we study a series of fundamental properties of probabilistic ω-automata with three different language-semantics: (1) the probable semantics that requires positive acceptance probability, (2) the almost-sure semantics that requires acceptance with probability 1, and (3) the threshold semantics that relies on an additional parameter λ i r0,1l that specifies a lower probability bound for the acceptance probability We provide a comparison of probabilistic ω-automata under these three semantics and nondeterministic ω-automata concerning expressiveness and efficiency Furthermore, we address closure properties under the Boolean operators union, intersection and complementation and algorithmic aspects, such as checking emptiness or language containment
396 citations
29 Jun 2009
TL;DR: It is shown that consistent models may not possess a single trace model whose objects can be read as traceability links in either direction, and proposed a simple game-theoretic semantics.
Abstract: The QVT Relations (QVT-R) transformation language allows the definition of bidirectional model transformations, which are required in cases where a two (or more) models must be kept consistent in the face of changes to either. A QVT-R transformation can be used either in checkonly mode, to determine whether a target model is consistent with a given source model, or in enforce mode, to change the target model. Although the most obvious semantic issues in the QVT standard concern the restoration of consistency, in fact even checkonly mode is not completely straightforward; this mode is the focus of this paper. We need to consider the overall structure of the transformation as given by when and where clauses, and the role of trace classes. In the standard, the semantics of QVT-R are given both directly, and by means of a translation to QVT Core, a language which is intended to be simpler. In this paper, we argue that there are irreconcilable differences between the intended semantics of QVT-R and those of QVT Core, so that the translation cannot be helpful. Treating QVT-R directly, we propose a simple game-theoretic semantics. We demonstrate that consistent models may not possess a single trace model whose objects can be read as traceability links in either direction. We briefly discuss the effect of variations in the rules of the game, to elucidate some design choices available to the designers of the QVT-R language.
269 citations
12 Aug 2006
TL;DR: This paper shows how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions and revisits Safra's determinization constructions.
Abstract: In this paper we revisit Safra's determinization constructions. We show how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions. Specifically, starting from a nondeterministic Buchi automaton with n states our construction yields a deterministic parity automaton with n2n+2 states and index 2n (instead of a Rabin automaton with (12)nn2n states and n pairs). Starting from a nondeterministic Streett automaton with n states and k pairs our construction yields a deterministic parity automaton with nn(k+2)+2(k+1)2n(K+1) states and index 2n(k+1) (instead of a Rabin automaton with (12)n(k+1)n n(k+2)(k+1)2n(k+1) states and n(k+1) pairs). The parity condition is much simpler than the Rabin condition. In applications such as solving games and emptiness of tree automata handling the Rabin condition involves an additional multiplier of n2n!(or(n(k+1))2(n(k+1))! in the case of Streett) which is saved using our construction
216 citations
TL;DR: This work uses a completely different, and elementary, approach to obtain a deterministic subexponential algorithm for the solution of parity games, and is almost as fast as the randomized algorithms mentioned above.
Abstract: The existence of polynomial-time algorithms for the solution of parity games is a major open problem. The fastest known algorithms for the problem are randomized algorithms that run in subexponential time. These algorithms are all ultimately based on the randomized subexponential simplex algorithms of Kalai and of Matousek, Sharir, and Welzl. Randomness seems to play an essential role in these algorithms. We use a completely different, and elementary, approach to obtain a deterministic subexponential algorithm for the solution of parity games. The new algorithm, like the existing randomized subexponential algorithms, uses only polynomial space, and it is almost as fast as the randomized subexponential algorithms mentioned above.
180 citations