15,907 research outputs found
Timed Parity Games: Complexity and Robustness
We consider two-player games played in real time on game structures with
clocks where the objectives of players are described using parity conditions.
The games are \emph{concurrent} in that at each turn, both players
independently propose a time delay and an action, and the action with the
shorter delay is chosen. To prevent a player from winning by blocking time, we
restrict each player to play strategies that ensure that the player cannot be
responsible for causing a zeno run. First, we present an efficient reduction of
these games to \emph{turn-based} (i.e., not concurrent) \emph{finite-state}
(i.e., untimed) parity games. Our reduction improves the best known complexity
for solving timed parity games. Moreover, the rich class of algorithms for
classical parity games can now be applied to timed parity games. The states of
the resulting game are based on clock regions of the original game, and the
state space of the finite game is linear in the size of the region graph.
Second, we consider two restricted classes of strategies for the player that
represents the controller in a real-time synthesis problem, namely,
\emph{limit-robust} and \emph{bounded-robust} winning strategies. Using a
limit-robust winning strategy, the controller cannot choose an exact
real-valued time delay but must allow for some nonzero jitter in each of its
actions. If there is a given lower bound on the jitter, then the strategy is
bounded-robust winning. We show that exact strategies are more powerful than
limit-robust strategies, which are more powerful than bounded-robust winning
strategies for any bound. For both kinds of robust strategies, we present
efficient reductions to standard timed automaton games. These reductions
provide algorithms for the synthesis of robust real-time controllers
Model-free reinforcement learning for stochastic parity games
This paper investigates the use of model-free reinforcement learning to compute the optimal value in two-player stochastic games with parity objectives. In this setting, two decision makers, player Min and player Max, compete on a finite game arena - a stochastic game graph with unknown but fixed probability distributions - to minimize and maximize, respectively, the probability of satisfying a parity objective. We give a reduction from stochastic parity games to a family of stochastic reachability games with a parameter ε, such that the value of a stochastic parity game equals the limit of the values of the corresponding simple stochastic games as the parameter ε tends to 0. Since this reduction does not require the knowledge of the probabilistic transition structure of the underlying game arena, model-free reinforcement learning algorithms, such as minimax Q-learning, can be used to approximate the value and mutual best-response strategies for both players in the underlying stochastic parity game. We also present a streamlined reduction from 112-player parity games to reachability games that avoids recourse to nondeterminism. Finally, we report on the experimental evaluations of both reductions
New Deterministic Algorithms for Solving Parity Games
We study parity games in which one of the two players controls only a small
number of nodes and the other player controls the other nodes of the
game. Our main result is a fixed-parameter algorithm that solves bipartite
parity games in time , and general parity games in
time , where is the number of distinct
priorities and is the number of edges. For all games with this
improves the previously fastest algorithm by Jurdzi{\'n}ski, Paterson, and
Zwick (SICOMP 2008). We also obtain novel kernelization results and an improved
deterministic algorithm for graphs with small average degree
Generic Model Checking for Modal Fixpoint Logics in COOL-MC
We report on COOL-MC, a model checking tool for fixpoint logics that is
parametric in the branching type of models (nondeterministic, game-based,
probabilistic etc.) and in the next-step modalities used in formulae. The tool
implements generic model checking algorithms developed in coalgebraic logic
that are easily adapted to concrete instance logics. Apart from the standard
modal -calculus, COOL-MC currently supports alternating-time, graded,
probabilistic and monotone variants of the -calculus, but is also
effortlessly extensible with new instance logics. The model checking process is
realized by polynomial reductions to parity game solving, or, alternatively, by
a local model checking algorithm that directly computes the extensions of
formulae in a lazy fashion, thereby potentially avoiding the construction of
the full parity game. We evaluate COOL-MC on informative benchmark sets.Comment: Full Version of VMCAI 2024 publicatio
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