Related papers: Least and greatest fixpoints in game semantics
Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…
We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
We present two methods to algorithmically compute both least and greatest solutions of polynomial equation systems over absorptive semirings (with certain completeness and continuity assumptions), such as the tropical semiring. Both methods…
We consider games played on an infinite probabilistic arena where the first player aims at satisfying generalized B\"uchi objectives almost surely, i.e., with probability one. We provide a fixpoint characterization of the winning sets and…
We analyze Coquand's game-theoretic interpretation of Peano Arithmetic through the lens of elementary descent recursion. In Coquand's game semantics, winning strategies correspond to infinitary cut-free proofs and cut elimination…
We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of…
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…
We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…
Infinite-state games provide a framework for the synthesis of reactive systems with unbounded data domains. Solving such games typically relies on computing symbolic fixpoints, particularly symbolic attractors. However, these computations…
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…
Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
We introduce the notions of w-lower semicontinuous and almost w-lower semicontinuous correspondence with respect to a given set and prove a new fixed-point theorem. We also introduce the notion of correspondence with e-LSCS-property. As…
Infinite-state games are a commonly used model for the synthesis of reactive systems with unbounded data domains. Symbolic methods for solving such games need to be able to construct intricate arguments to establish the existence of winning…
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically…
In this article, we consider some simple combinatorial game and a winning strategy in this game. This game is then used to prove several known results about non-repetitive sequences and approximations with denominators from a lacunary…
Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model…
We present a fixpoint semantics of event systems. The semantics is presented in a general framework without concerns of fairness. Soundness and completeness of rules for deriving "leads-to" properties are proved in this general framework.…