911 research outputs found
Average-energy games
Two-player quantitative zero-sum games provide a natural framework to
synthesize controllers with performance guarantees for reactive systems within
an uncontrollable environment. Classical settings include mean-payoff games,
where the objective is to optimize the long-run average gain per action, and
energy games, where the system has to avoid running out of energy.
We study average-energy games, where the goal is to optimize the long-run
average of the accumulated energy. We show that this objective arises naturally
in several applications, and that it yields interesting connections with
previous concepts in the literature. We prove that deciding the winner in such
games is in NP inter coNP and at least as hard as solving mean-payoff games,
and we establish that memoryless strategies suffice to win. We also consider
the case where the system has to minimize the average-energy while maintaining
the accumulated energy within predefined bounds at all times: this corresponds
to operating with a finite-capacity storage for energy. We give results for
one-player and two-player games, and establish complexity bounds and memory
requirements.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Non-Zero Sum Games for Reactive Synthesis
In this invited contribution, we summarize new solution concepts useful for
the synthesis of reactive systems that we have introduced in several recent
publications. These solution concepts are developed in the context of non-zero
sum games played on graphs. They are part of the contributions obtained in the
inVEST project funded by the European Research Council.Comment: LATA'16 invited pape
Liveness of Randomised Parameterised Systems under Arbitrary Schedulers (Technical Report)
We consider the problem of verifying liveness for systems with a finite, but
unbounded, number of processes, commonly known as parameterised systems.
Typical examples of such systems include distributed protocols (e.g. for the
dining philosopher problem). Unlike the case of verifying safety, proving
liveness is still considered extremely challenging, especially in the presence
of randomness in the system. In this paper we consider liveness under arbitrary
(including unfair) schedulers, which is often considered a desirable property
in the literature of self-stabilising systems. We introduce an automatic method
of proving liveness for randomised parameterised systems under arbitrary
schedulers. Viewing liveness as a two-player reachability game (between
Scheduler and Process), our method is a CEGAR approach that synthesises a
progress relation for Process that can be symbolically represented as a
finite-state automaton. The method is incremental and exploits both
Angluin-style L*-learning and SAT-solvers. Our experiments show that our
algorithm is able to prove liveness automatically for well-known randomised
distributed protocols, including Lehmann-Rabin Randomised Dining Philosopher
Protocol and randomised self-stabilising protocols (such as the Israeli-Jalfon
Protocol). To the best of our knowledge, this is the first fully-automatic
method that can prove liveness for randomised protocols.Comment: Full version of CAV'16 pape
Obligation Blackwell Games and p-Automata
We recently introduced p-automata, automata that read discrete-time Markov
chains. We used turn-based stochastic parity games to define acceptance of
Markov chains by a subclass of p-automata. Definition of acceptance required a
cumbersome and complicated reduction to a series of turn-based stochastic
parity games. The reduction could not support acceptance by general p-automata,
which was left undefined as there was no notion of games that supported it.
Here we generalize two-player games by adding a structural acceptance
condition called obligations. Obligations are orthogonal to the linear winning
conditions that define winning. Obligations are a declaration that player 0 can
achieve a certain value from a configuration. If the obligation is met, the
value of that configuration for player 0 is 1.
One cannot define value in obligation games by the standard mechanism of
considering the measure of winning paths on a Markov chain and taking the
supremum of the infimum of all strategies. Mainly because obligations need
definition even for Markov chains and the nature of obligations has the flavor
of an infinite nesting of supremum and infimum operators. We define value via a
reduction to turn-based games similar to Martin's proof of determinacy of
Blackwell games with Borel objectives. Based on this definition, we show that
games are determined. We show that for Markov chains with Borel objectives and
obligations, and finite turn-based stochastic parity games with obligations
there exists an alternative and simpler characterization of the value function.
Based on this simpler definition we give an exponential time algorithm to
analyze finite turn-based stochastic parity games with obligations. Finally, we
show that obligation games provide the necessary framework for reasoning about
p-automata and that they generalize the previous definition
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