89 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
On the equivalence of game and denotational semantics for the probabilistic mu-calculus
The probabilistic (or quantitative) modal mu-calculus is a fixed-point logic
de- signed for expressing properties of probabilistic labeled transition
systems (PLTS). Two semantics have been studied for this logic, both assigning
to every process state a value in the interval [0,1] representing the
probability that the property expressed by the formula holds at the state. One
semantics is denotational and the other is a game semantics, specified in terms
of two-player stochastic games. The two semantics have been proved to coincide
on all finite PLTS's, but the equivalence of the two semantics on arbitrary
models has been open in literature. In this paper we prove that the equivalence
indeed holds for arbitrary infinite models, and thus our result strengthens the
fruitful connection between denotational and game semantics. Our proof adapts
the unraveling or unfolding method, a general proof technique for proving
result of parity games by induction on their complexity
Blackwell-Optimal Strategies in Priority Mean-Payoff Games
We examine perfect information stochastic mean-payoff games - a class of
games containing as special sub-classes the usual mean-payoff games and parity
games. We show that deterministic memoryless strategies that are optimal for
discounted games with state-dependent discount factors close to 1 are optimal
for priority mean-payoff games establishing a strong link between these two
classes
One-Counter Stochastic Games
We study the computational complexity of basic decision problems for
one-counter simple stochastic games (OC-SSGs), under various objectives.
OC-SSGs are 2-player turn-based stochastic games played on the transition graph
of classic one-counter automata. We study primarily the termination objective,
where the goal of one player is to maximize the probability of reaching counter
value 0, while the other player wishes to avoid this. Partly motivated by the
goal of understanding termination objectives, we also study certain "limit" and
"long run average" reward objectives that are closely related to some
well-studied objectives for stochastic games with rewards. Examples of problems
we address include: does player 1 have a strategy to ensure that the counter
eventually hits 0, i.e., terminates, almost surely, regardless of what player 2
does? Or that the liminf (or limsup) counter value equals infinity with a
desired probability? Or that the long run average reward is >0 with desired
probability? We show that the qualitative termination problem for OC-SSGs is in
NP intersection coNP, and is in P-time for 1-player OC-SSGs, or equivalently
for one-counter Markov Decision Processes (OC-MDPs). Moreover, we show that
quantitative limit problems for OC-SSGs are in NP intersection coNP, and are in
P-time for 1-player OC-MDPs. Both qualitative limit problems and qualitative
termination problems for OC-SSGs are already at least as hard as Condon's
quantitative decision problem for finite-state SSGs.Comment: 20 pages, 1 figure. This is a full version of a paper accepted for
publication in proceedings of FSTTCS 201
Limit Your Consumption! Finding Bounds in Average-energy Games
Energy games are infinite two-player games played in weighted arenas with
quantitative objectives that restrict the consumption of a resource modeled by
the weights, e.g., a battery that is charged and drained. Typically, upper
and/or lower bounds on the battery capacity are part of the problem
description. Here, we consider the problem of determining upper bounds on the
average accumulated energy or on the capacity while satisfying a given lower
bound, i.e., we do not determine whether a given bound is sufficient to meet
the specification, but if there exists a sufficient bound to meet it.
In the classical setting with positive and negative weights, we show that the
problem of determining the existence of a sufficient bound on the long-run
average accumulated energy can be solved in doubly-exponential time. Then, we
consider recharge games: here, all weights are negative, but there are recharge
edges that recharge the energy to some fixed capacity. We show that bounding
the long-run average energy in such games is complete for exponential time.
Then, we consider the existential version of the problem, which turns out to be
solvable in polynomial time: here, we ask whether there is a recharge capacity
that allows the system player to win the game.
We conclude by studying tradeoffs between the memory needed to implement
strategies and the bounds they realize. We give an example showing that memory
can be traded for bounds and vice versa. Also, we show that increasing the
capacity allows to lower the average accumulated energy.Comment: In Proceedings QAPL'16, arXiv:1610.0769
A survey of stochastic ω regular games
We summarize classical and recent results about two-player games played on graphs with ω-regular objectives. These games have applications in the verification and synthesis of reactive systems. Important distinctions are whether a graph game is turn-based or concurrent; deterministic or stochastic; zero-sum or not. We cluster known results and open problems according to these classifications
One-To-Two-Player Lifting for Mildly Growing Memory
We investigate a phenomenon of "one-to-two-player lifting" in infinite-duration two-player games on graphs with zero-sum objectives. More specifically, let ? be a class of strategies. It turns out that in many cases, to show that all two-player games on graphs with a given payoff function are determined in ?, it is sufficient to do so for one-player games. That is, in many cases the determinacy in ? can be "lifted" from one-player games to two-player games. Namely, Gimbert and Zielonka (CONCUR 2005) have shown this for the class of positional strategies. Recently, Bouyer et al. (CONCUR 2020) have extended this to the classes of arena-independent finite-memory strategies. Informally, these are finite-memory strategies that use the same way of storing memory in all game graphs.
In this paper, we put the lifting technique into the context of memory complexity. The memory complexity of a payoff function measures, how many states of memory we need to play optimally in game graphs with up to n nodes, depending on n. We address the following question. Assume that we know the memory complexity of our payoff function in one-player games. Then what can be said about its memory complexity in two-player games? In particular, when is it finite?
In this paper, we answer this questions for strategies with "chromatic" memory. These are strategies that only accumulate sequences of colors of edges in their memory. We obtain the following results.
- Assume that the chromatic memory complexity in one-player games is sublinear in n on some infinite subsequence. Then the chromatic memory complexity in two-player games is finite.
- We provide an example in which (a) the chromatic memory complexity in one-player games is linear in n; (b) the memory complexity in two-player games is infinite. Thus, we obtain the exact barrier for the one-to-two-player lifting theorems in the setting of chromatic finite-memory strategies. Previous results only cover payoff functions with constant chromatic memory complexity
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