Related papers: Determinacy separations for class games
This paper investigates some necessary and sufficient conditions for a game to be a potential game. At first, we extend the classical results of Slade and Monderer and Shapley from games with one-dimensional action spaces to games with…
Different constructions in the recursion theory use the so-called priority arguments. A general scheme was suggested by A.~Lachlan. Based on his work, we define the notion of a priority-closed class of requirements. Then, for a specific…
We consider the reachability problem for higher-order functional programs and study the relationship between reachability games (i.e., the reachability problem for programs with angelic and demonic nondeterminism) and may-reachability…
We investigate forms of filter extension properties in the two-cardinal setting involving filters on $P_\kappa(\lambda)$. We generalize the filter games introduced by Holy and Schlicht in \cite{HolySchlicht:HierarchyRamseyLikeCardinals} to…
We present a formalization of Borel determinacy in the Lean 4 theorem prover. The formalization includes a definition of Gale-Stewart games and a proof of Martin's theorem stating that Borel games are determined. The proof closely follows…
We study algorithmic complexity of solving subtraction games in a~fixed dimension with a finite difference set. We prove that there exists a game in this class such that any algorithm solving the game runs in exponential time. Also we prove…
We give an elementary proof that in a Borel family of games, the set of games for which player II has a winning strategy is Baire measurable, universally measurable, and completely Ramsey in the case where $X = [\mathbb{N}]^{\aleph_0}$.
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
We prove that the problem of deciding the consequence relation of the full Lambek calculus with weakening is complete for the class HAck of hyper-Ackermannian problems (i.e., level F_{\omega}^{\omega} of the ordinal-indexed hierarchy of…
Making classifiers robust to adversarial examples is hard. Thus, many defenses tackle the seemingly easier task of detecting perturbed inputs. We show a barrier towards this goal. We prove a general hardness reduction between detection and…
Determining a Nash equilibrium in a $2$-player non-zero sum game is known to be PPAD-hard (Chen and Deng (2006), Chen, Deng and Teng (2009)). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and…
Morrill and Valentin in the paper "Computational coverage of TLG: Nonlinearity" considered an extension of the Lambek calculus enriched by a so-called "exponential" modality. This modality behaves in the "relevant" style, that is, it allows…
Berlekamp proposed a class of impartial combinatorial games based on the moves of chess pieces on rectangular boards. We generalize impartial chess games by playing them on Young diagrams and obtain results about winning and losing…
We consider a class of nonlocal games that are related to binary constraint systems (BCSs) in a manner similar to the games implicit in the work of Mermin [N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems," Phys.…
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…
We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal…
We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal…
Exacting and ultraexacting cardinals are large cardinal numbers compatible with the Zermelo-Fraenkel axioms of set theory, including the Axiom of Choice. In contrast with standard large cardinal notions, their existence implies that the…
We prove that the class of all ordinals Ord is not weakly compact with respect to definable classes. Specifically, in any model of ZFC, the definable tree property fails for Ord, in that there is a definable Ord tree with no definable…
We introduce a new, game-theoretic approach to anti-classification results for orbit equivalence relations. Within this framework, we give a short conceptual proof of Hjorth's turbulence theorem. We also introduce a new dynamical criterion…