On Omega-Languages Defined by Mean-Payoff Conditions

Alur, Rajeev; Degorre, Aldric; Maler, Oded; Weiss, Gera

doi:10.1007/978-3-642-00596-1_24

Cited by 24 publications

(47 citation statements)

References 14 publications

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“…In [4], new classes of cost functions were studied using operations over rational numbers that do not form a semiring. In [5], deterministic weighted automata with mean-payoff objectives were further studied, providing closure under Boolean operations. Several other works have considered quantitative generalizations of languages, over finite words [15], over trees [16], or using finite lattices [17], [18].…”

Section: Long Run Happiness Consider a System With Boolean Variablesmentioning

confidence: 99%

“…The problem for Kripke structures without fairness was solved in [5] 4 For extending the technique there to Kripke structures with fairness, we first need the following lemma. It intuitively shows that inserting infinitely, but negligibly, many constant values to a computation does not change its limit-average values.…”

Section: Given An Ltlmentioning

confidence: 99%

“…1 There has recently been a significant effort to study such quantitative-oriented specification. The approach that has been mostly followed is to consider specific objectives, as meanpayoff or energy-level, by means of weighted automata [3], [4], [5], [6]. No attention, however, has been put in extending temporal logics to provide a general framework for quantitative-oriented specifications.…”

Section: Introductionmentioning

confidence: 99%

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Temporal Specifications with Accumulative Values

Boker

Chatterjee

Henzinger

et al. 2011

2011 IEEE 26th Annual Symposium on Logic in Computer Science

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Abstract-There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications.In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation.We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with "controlled-accumulation", allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.

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Section: Long Run Happiness Consider a System With Boolean Variablesmentioning

confidence: 99%

Section: Given An Ltlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Temporal Specifications with Accumulative Values

Boker

Chatterjee

Henzinger

et al. 2011

2011 IEEE 26th Annual Symposium on Logic in Computer Science

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“…This problem has tight connection (through polynomial-time reductions) with important theoretical questions about logics and games, such as the µ-calculus model-checking, and solving parity games [13,14,17,18]. Second, quantitative objectives in general are gaining interest in the specification and design of reactive systems [8,5,11], where the weights represent resource usage (e.g., energy consumption or network usage); the problem of controller synthesis with resource constraints requires the solution of quantitative games [20,6,1,3]. Finally, mean-payoff games are log-space equivalent to energy games (EG) where the objective of Player 1 is to maintain the sum of the weight (called the energy level) positive, given a fixed initial credit of energy.…”

Section: Introductionmentioning

confidence: 99%

Energy and Mean-Payoff Games with Imperfect Information

Degorre

Doyen

Gentilini

et al. 2010

Computer Science Logic

Self Cite

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Abstract. We consider two-player games with imperfect information and quantitative objective. The game is played on a weighted graph with a state space partitioned into classes of indistinguishable states, giving players partial knowledge of the state. In an energy game, the weights represent resource consumption and the objective of the game is to maintain the sum of weights always nonnegative. In a mean-payoff game, the objective is to optimize the limit-average usage of the resource. We show that the problem of determining if an energy game with imperfect information with fixed initial credit has a winning strategy is decidable, while the question of the existence of some initial credit such that the game has a winning strategy is undecidable. This undecidability result carries over to mean-payoff games with imperfect information. On the positive side, using a simple restriction on the game graph (namely, that the weights are visible), we show that these problems become EXPTIME-complete.

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“…For finite automata, mean-payoff conditions have been investigated [10,1,9]: with each run is associated the limit average of weights encountered along the execution. Our notion of frequency extends mean-payoff conditions to timed systems by assigning to an execution the limit average of time spent in some distinguished locations.…”

Section: Introductionmentioning

confidence: 99%

Emptiness and Universality Problems in Timed Automata with Positive Frequency

Bertrand

Bouyer

Brihaye

et al. 2011

Automata, Languages and Programming

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Abstract. The languages of infinite timed words accepted by timed automata are traditionally defined using Büchi-like conditions. These acceptance conditions focus on the set of locations visited infinitely often along a run, but completely ignore quantitative timing aspects. In this paper we propose a natural quantitative semantics for timed automata based on the so-called frequency, which measures the proportion of time spent in the accepting locations. We study various properties of timed languages accepted with positive frequency, and in particular the emptiness and universality problems.

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On Omega-Languages Defined by Mean-Payoff Conditions

Cited by 24 publications

References 14 publications

Temporal Specifications with Accumulative Values

Temporal Specifications with Accumulative Values

Energy and Mean-Payoff Games with Imperfect Information

Emptiness and Universality Problems in Timed Automata with Positive Frequency

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