Weak alternating automata give a simple explanation of why most temporal and dynamic logics are decidable in exponential time

Muller, David E.; Saoudi, A.; Schupp, Paul E.

doi:10.1109/lics.1988.5139

Cited by 58 publications

(54 citation statements)

References 7 publications

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“…Moreover, it generates a stand-alone program that can be used independently of any particular proof assistant. The second author [11] previously presented a formalisation of weak alternating automata (WAA [12]), including a translation of LTL formulae into WAA. Due to their much richer combinatorial structure, WAA afford a rather straightforward LTL translation of linear complexity, whereas the translation into (generalised) Büchi automata is exponential.…”

Section: Resultsmentioning

confidence: 99%

Construction of Büchi Automata for LTL Model Checking Verified in Isabelle/HOL

Schimpf

Merz

Smaus

2009

Lecture Notes in Computer Science

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Abstract. We present the implementation in Isabelle/HOL of a translation of LTL formulae into Büchi automata. In automaton-based model checking, systems are modelled as transition systems, and correctness properties stated as formulae of temporal logic are translated into corresponding automata. An LTL formula is represented by a (generalised) Büchi automaton that accepts precisely those behaviours allowed by the formula. The model checking problem is then reduced to checking language inclusion between the two automata. The automaton construction is thus an essential component of an LTL model checking algorithm. We implemented a standard translation algorithm due to Gerth et al. The correctness and termination of our implementation are proven in Isabelle/HOL, and executable code is generated using the Isabelle/HOL code generator.

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Section: Resultsmentioning

confidence: 99%

Construction of Büchi Automata for LTL Model Checking Verified in Isabelle/HOL

Schimpf

Merz

Smaus

2009

Lecture Notes in Computer Science

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“…An alternating Büchi automaton [2,10] is a tuple A = (S, Σ, s 0 , ρ, F ), where S is a finite nonempty set of states, Σ is a finite nonempty alphabet, s 0 ∈ S is the initial state, and F ⊆ S is the set of accepting states. The automaton can move from one state when it reads a symbol from Σ according to the transition function ρ : S × Σ → B + (S).…”

Section: Semantics On Respecting Tracesmentioning

confidence: 99%

Run-Time Monitoring of Electronic Contracts

Kyas

Prisacariu

Schneider

2008

Automated Technology for Verification and Analysis

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Abstract. Electronic inter-organizational relationships are governed by contracts regulating their interaction. It is necessary to run-time monitor the contracts, as to guarantee their fulfillment. The present work shows how to obtain a run-time monitor for contracts written in CL, a formal specification language which allows to write conditional obligations, permissions and prohibitions over actions. The trace semantics of CL formalizes the notion of a trace fulfills a contract. We show how to obtain, for a given contract, an alternating Büchi automaton which accepts exactly the traces that fulfill the contract. This automaton is the basis for obtaining a finite state machine which acts as a run-time monitor for CL contracts.

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“…Only a few years ago, the alternating 1-weak Büchi automata (or A1W automata for short, also known as alternating linear automata or very weak alternating automata) have been identified as the type of automata with the same expressive power as LTL. Muller, Saoudi, and Schupp [1] have introduced a translation of LTL formulae into equivalent A1W automata. The translation of A1W automata into equivalent LTL formulae has been presented independently by Rohde [2], and Löding and Thomas [3].…”

Section: Introductionmentioning

confidence: 99%

“…It is known that Linear Temporal Logic (LTL) has the same expressive power as alternating 1-weak automata (A1W automata, also called alternating linear automata or very weak alternating automata). A translation of LTL formulae into a language equivalent A1W automata has been introduced in [1]. The inverse translation has been developed independently in [2] and [3].…”

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confidence: 99%

Deeper Connections Between LTL and Alternating Automata

Pelánek

Strejček

2006

Implementation and Application of Automata

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Abstract. It is known that Linear Temporal Logic (LTL) has the same expressive power as alternating 1-weak automata (A1W automata, also called alternating linear automata or very weak alternating automata). A translation of LTL formulae into a language equivalent A1W automata has been introduced in [1]. The inverse translation has been developed independently in [2] and [3]. In the first part of the paper we show that the latter translation wastes temporal operators and we propose some improvements of this translation. The second part of the paper draws a direct connection between fragments of the Until-Release hierarchy [4] and alternation depth of nonaccepting and accepting states in A1W automata. We also indicate some corollaries and applications of these results.

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Weak alternating automata give a simple explanation of why most temporal and dynamic logics are decidable in exponential time

Cited by 58 publications

References 7 publications

Construction of Büchi Automata for LTL Model Checking Verified in Isabelle/HOL

Construction of Büchi Automata for LTL Model Checking Verified in Isabelle/HOL

Run-Time Monitoring of Electronic Contracts

Deeper Connections Between LTL and Alternating Automata

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