Open Implication

Greimel, Karin; Bloem, Roderick; Jobstmann, Barbara; Vardi, Moshe Y.

doi:10.1007/978-3-540-70583-3_30

Cited by 13 publications

(13 citation statements)

References 22 publications

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“…Since, however, T generates w, which is not in L, it does not realize L, contradicting the fact that L and L are open equivalent. We note that, by [5], the existence of an infinite transducer that distinguishes between L and L implies the existence of such a finite transducer.…”

Section: Black (L) Is Black Safementioning

confidence: 94%

“…While L and black (L) are not equivalent, they are open equivalent, in the sense of [5]. Formally, we have the following.…”

Section: Black (L) Is Black Safementioning

confidence: 99%

“…Most notably, the synthesis challenge, of generating a system that satisfies the specification, corresponds to the satisfiability problem in the closed setting and to the realizability problem in the open setting. As another example, the equivalence problem between LTL specifications is different in the closed and open settings [5]. That is, two specifications may not be equivalent when compared with respect to arbitrary systems on I ∪ O, but be open equivalent; that is, equivalent when compared with respect to I/O-transducers.…”

Section: Introductionmentioning

confidence: 99%

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Environment-Friendly Safety

Kupferman

Weiner

2013

Hardware and Software: Verification and Testing

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Abstract. Of special interest in verification are safety properties, which assert that the system always stays within some allowed region. For closed systems, the theoretical properties of safety properties as well as their practical advantages with respect to general properties are well understood. For open (a.k.a. reactive) systems, whose behavior depends on their on-going interaction with the environment, the common practice is to use the definition and algorithms of safety for closed systems, ignoring the distinction between input and output signals. In a recent work, Ehlers and Finkbeiner introduced reactive safety -a definition of safety for the setting of open systems. Essentially, reactive safety properties require the system to stay in a region of states that is both allowed and from which the environment cannot force it out. In this paper we continue their study and extend it to other families of properties. In the setting of closed systems, each safety property induces a set of finite bad prefixes -ones after which the property must be violated. The notion of bad prefixes enables a reduction of reasoning about safety properties to reasoning about properties of finite computations. We study reactive bad prefixes, their detection in theory and in practice, and their approximation by either a non-reactive safety property or by reasoning about the syntax of the formula. We study the dual notion, of reactive co-safety properties, and the corresponding theory of reactive good prefixes. For both safety and co-safety properties, we relate the definitions in the closed and open settings, and argue that our approach strictly extends the range of properties for which we can apply algorithms that are based on finite computations. Since the reactive setting is particularly challenging for general properties, such an application is significant in practice.

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Section: Black (L) Is Black Safementioning

confidence: 94%

“…While L and black (L) are not equivalent, they are open equivalent, in the sense of [5]. Formally, we have the following.…”

Section: Black (L) Is Black Safementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Environment-Friendly Safety

Kupferman

Weiner

2013

Hardware and Software: Verification and Testing

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“…Indeed, the strategy that outputs a grant after each req realizes φ but it does not realize ♦grant, as this strategy relies on the behavior of the environment. Thus dropping assumption is weaker than the notion of open implication of [13], which requires that the strategies realizing φ have to realize ♦grant.…”

Section: Theorem 9 Letmentioning

confidence: 99%

Antichains and compositional algorithms for LTL synthesis

Filiot

Jin

Raskin

2011

Form Methods Syst Des

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In this paper, we present new monolithic and compositional algorithms to solve the LTL realizability problem. Those new algorithms are based on a reduction of the LTL realizability problem to a game whose winning condition is defined by a universal automaton on infinite words with a k-co-Büchi acceptance condition. This acceptance condition asks that runs visit at most k accepting states, so it implicitly defines a safety game. To obtain efficient algorithms from this construction, we need several additional ingredients. First, we study the structure of the underlying automata constructions, and we show that there exists a partial order that structures the state space of the underlying safety game. This partial order can be used to define an efficient antichain algorithm. Second, we show that the algorithm can be implemented in an incremental way by considering increasing values of k in the acceptance condition. Finally, we show that for large LTL formulas that are written as conjunctions of smaller formulas, we can solve the problem compositionally by first computing winning strategies for each conjunct that appears in the large formula. We report on the behavior of those algorithms on several benchmarks. We show that the compositional algorithms are able to handle LTL formulas that are several pages long.

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“…Indeed, the strategy that outputs a grant after each req realizes φ but it does not realize ♦grant, as this strategy relies on the behavior of the environment. Thus dropping assumption is weaker than the notion of open implication of [8], which requires that the strategies realizing φ have to realize ♦grant.…”

Section: Theorem 4 Letmentioning

confidence: 99%

Compositional Algorithms for LTL Synthesis

Filiot

Jin

Raskin

2010

Automated Technology for Verification and Analysis

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Abstract. In this paper, we provide two compositional algorithms to solve safety games and apply them to provide compositional algorithms for the LTL synthesis problem. We have implemented those new compositional algorithms, and we demonstrate that they are able to handle full LTL specifications that are orders of magnitude larger than the specifications that can be treated by the current state of the art algorithms.

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Open Implication

Cited by 13 publications

References 22 publications

Environment-Friendly Safety

Environment-Friendly Safety

Antichains and compositional algorithms for LTL synthesis

Compositional Algorithms for LTL Synthesis

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