Promptness in ω-Regular Automata

Almagor, Shaull; Hirshfeld, Yoram; Kupferman, Orna

doi:10.1007/978-3-642-15643-4_4

Cited by 8 publications

(8 citation statements)

References 23 publications

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“…On the other hand, in many applications, it is important to bound the wait time. In the last decade, many papers have focused on quantitative aspects, in particular boundedness requirements, of formal verification [1,19,10], including parity games [10,15,23,24]. In [19], the authors introduce Prompt LTL, an extension of standard LTL [25] with the prompt-eventually operator F p : a finite system satisfies a Prompt LTL formula ϕ iff there is a bound on the wait time for all the prompt-eventually subformulas of ϕ in all the computations of the system.…”

Section: Introductionmentioning

confidence: 99%

“…In [19], the authors introduce Prompt LTL, an extension of standard LTL [25] with the prompt-eventually operator F p : a finite system satisfies a Prompt LTL formula ϕ iff there is a bound on the wait time for all the prompt-eventually subformulas of ϕ in all the computations of the system. The automata-theoretic counterpart of the F p operator has been investigated in [1]. Parity games extended with promptness requirements, the so-called finitary parity games, have been studied in [10].…”

Section: Introductionmentioning

confidence: 99%

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Hierarchical cost-parity games

Bozzelli

Murano

Perelli

et al. 2020

Theoretical Computer Science

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Cost-parity games are a fundamental tool in system design for the analysis of reactive and distributed systems that recently have received a lot of attention from the formal methods research community. They allow to reason about the time delay on the requests granted by systems, with a bounded consumption of resources, in their executions.In this paper, we contribute to research on Cost-parity games by combining them with hierarchical systems, a successful method for the succinct representation of models. We show that determining the winner of a Hierarchical Cost-parity Game is PSpace-complete, thus matching the complexity of the proper special case of Hierarchical Parity Games. This shows that reasoning about temporal delay can be addressed at a free cost in terms of complexity.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hierarchical cost-parity games

Bozzelli

Murano

Perelli

et al. 2020

Theoretical Computer Science

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“…In [19], it has been addressed by forcing Ltl to express "prompt" requirements, by means of a prompt operator F p added to the logic. In [1] the automata-theoretic counterpart of the F p operator has been studied. In particular, prompt-Büchi automata are introduced and it has been showed that their intersection with ω-regular languages is equivalent to co-Büchi.…”

Section: Introductionmentioning

confidence: 99%

On Promptness in Parity Games*†

Mogavero

Murano

Sorrentino

2015

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Abstract. Parity games are a powerful formalism for the automatic synthesis and verification of reactive systems. They are closely related to alternating ω-automata and emerge as a natural method for the solution of the µ-calculus model checking problem. Due to these strict connections, parity games are a well-established environment to describe liveness properties such as "every request that occurs infinitely often is eventually responded". Unfortunately, the classical form of such a condition suffers from the strong drawback that there is no bound on the effective time that separates a request from its response, i.e., responses are not promptly provided. Recently, to overcome this limitation, several parity game variants have been proposed, in which quantitative requirements are added to the classic qualitative ones. In this paper, we make a general study of the concept of promptness in parity games that allows to put under a unique theoretical framework several of the cited variants along with new ones. Also, we describe simple polynomial reductions from all these conditions to either Büchi or parity games, which simplify all previous known procedures. In particular, they improve the complexity results of cost and bounded-cost parity games. Indeed, we provide solution algorithms showing that determining the winner of these games lies in UPTime ∩ CoUPTime.

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“…In this paper we study temporal quality as well as the combinations of both aspects. One may try to reduce temporal quality to propositional quality by a repeated use of the X ("next") operator or by a use of bounded (prompt) eventualities [2,3]. Both approaches, however, partitions the future into finitely many zones and are limited: correctness of LTL is Boolean, and thus has inherent dichotomy between satisfaction and dissatisfaction.…”

Section: Introductionmentioning

confidence: 99%

Discounting in LTL

Almagor

Boker

Kupferman

2014

Tools and Algorithms for the Construction and Analysis of Systems

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In recent years, there is growing need and interest in formalizing and reasoning about the quality of software and hardware systems. As opposed to traditional verification, where one handles the question of whether a system satisfies, or not, a given specification, reasoning about quality addresses the question of how well the system satisfies the specification. One direction in this effort is to refine the "eventually" operators of temporal logic to discounting operators: the satisfaction value of a specification is a value in [0, 1], where the longer it takes to fulfill eventuality requirements, the smaller the satisfaction value is. In this paper we introduce an augmentation by discounting of Linear Temporal Logic (LTL), and study it, as well as its combination with propositional quality operators. We show that one can augment LTL with an arbitrary set of discounting functions, while preserving the decidability of the model-checking problem. Further augmenting the logic with unary propositional quality operators preserves decidability, whereas adding an average-operator makes some problems undecidable. We also discuss the complexity of the problem, as well as various extensions.LTL disc [D] is actually a family of logics, each parameterized by a set D of discounting functions -strictly decreasing functions from AE to [0, 1] that tend to 0 (e.g., linear decaying, exponential decaying, etc.). LTL disc [D] includes a discounting-"until" (U η ) operator, parameterized by a function η ∈ D. We solve the model-checking threshold problem for LTL disc [D]: given a Kripke structure K, an LTL disc [D] formula ϕ and a threshold t ∈ [0, 1], the algorithm decides whether the satisfaction value of ϕ in K is at least t.In the Boolean setting, the automata-theoretic approach has proven to be very useful in reasoning about LTL specifications. The approach is based on translating LTL formulas to nondeterministic Büchi automata on infinite words [28]. Applying this approach to the discounted setting, which gives rise to infinitely many satisfaction values, poses a big algorithmic challenge: model-checking algorithms, and in particular those that follow the automata-theoretic approach, are based on an exhaustive search, which cannot be simply applied when the domain becomes infinite. A natural relevant extension to the automata-theoretic approach is to translate formulas to weighted automata [22]. Unfortunately, these extensively-studied models are complicated and many problems become undecidable for them [15]. We show that for threshold problems, we can translate LTL disc [D] formulas into (Boolean) nondeterministic Büchi automata, with the property that the automaton accepts a lasso computation iff the formula attains a value above the threshold on that computation. Our algorithm relies on the fact that the language of an automaton is non-empty iff there is a lasso witness for the non-emptiness. We cope with the infinitely many possible satisfaction values by using the discounting behavior of the eventualities and the given thre...

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Promptness in ω-Regular Automata

Cited by 8 publications

References 23 publications

Hierarchical cost-parity games

Hierarchical cost-parity games

On Promptness in Parity Games*†

Discounting in LTL

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