相关论文: Generating and Solving Symbolic Parity Games

Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…

Symbolic encoding has been used in multi-operator learning as a way to embed additional information for distinct time-series data. For spatiotemporal systems described by time-dependent partial differential equations, the equation itself…

We study nondeterministic strategies in parity games with the aim of computing a most permissive winning strategy. Following earlier work, we measure permissiveness in terms of the average number/weight of transitions blocked by the…

Algorithms for model checking and satisfiability of the modal $\mu$-calculus start by converting formulas to alternating parity tree automata. Thus, model checking is reduced to checking acceptance by tree automata and satisfiability to…

Petri games are a multiplayer game model for the automatic synthesis of distributed systems. We compare two fundamentally different approaches for solving Petri games. The symbolic approach decides the existence of a winning strategy via a…

Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…

We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…

Emerson-Lei conditions have recently attracted attention due to their succinctness and compositionality properties. In the current work, we show how infinite-duration games with Emerson-Lei objectives can be analyzed in two different ways.…

We present a method for solving implicit (factored) Markov decision processes (MDPs) with very large state spaces. We introduce a property of state space partitions which we call epsilon-homogeneity. Intuitively, an epsilon-homogeneous…

Information design (ID) explores how a sender influence the optimal behavior of receivers to achieve specific objectives. While ID originates from everyday human communication, existing game-theoretic and machine learning methods often…

Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their…

Training models through self-play alone (without any human data) has been a longstanding goal in AI, but its effectiveness for training large language models remains unclear, particularly in code generation where rewards based on unit tests…

Motivated by the remarkable success of artificial intelligence (AI) across diverse fields, the application of AI to solve scientific problems, often formulated as partial differential equations (PDEs), has garnered increasing attention.…

We introduce a natural notion of limit-deterministic parity automata and present a method that uses such automata to construct satisfiability games for the weakly aconjunctive fragment of the $\mu$-calculus. To this end we devise a method…

Parity games have been broadly studied in recent years for their applications to controller synthesis and verification. In practice, partial solvers for parity games that execute in polynomial time, while incomplete, can solve most games in…

Parity games play a central role in model checking and satisfiability checking. Solving parity games is computationally expensive, among others due to the size of the games, which, for model checking problems, can easily contain $10^9$…

Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…

BDDs are representations of a Boolean expression in the form of a directed acyclic graph. BDDs are widely used in several fields, particularly in model checking and hardware verification. There are several implementations for BDD…

Stochastic games are a convenient formalism for modelling systems that comprise rational agents competing or collaborating within uncertain environments. Probabilistic model checking techniques for this class of models allow us to formally…

Parikh's game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone…