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Mathematical reasoning is central to artificial intelligence, with applications in education, code generation, and research-level mathematical discovery. Mathematical competitions highlight two problem types: theorem proving, requiring…
We study single-player extensive-form games with imperfect recall, such as the Sleeping Beauty problem or the Absentminded Driver game. For such games, two natural equilibrium concepts have been proposed as alternative solution concepts to…
One way of suggesting that an NP problem may not be NP-complete is to show that it is in the class UP. We suggest an analogous new approach---weaker in strength of evidence but more broadly applicable---to suggesting that concrete~NP…
The ability to deploy neural networks in real-world, safety-critical systems is severely limited by the presence of adversarial examples: slightly perturbed inputs that are misclassified by the network. In recent years, several techniques…
Multi-agent learning is a challenging problem in machine learning that has applications in different domains such as distributed control, robotics, and economics. We develop a prescriptive model of multi-agent behavior using Markov games.…
Parity games are two player games with omega-winning conditions, played on finite graphs. Such games play an important role in verification, satisfiability and synthesis. It is therefore important to identify algorithms that can efficiently…
Group polarization, the phenomenon where individuals become more extreme after interacting, has been gaining attention, especially with the rise of social media shaping people's opinions. Recent interest has emerged in formal reasoning…
The Tree Evaluation Problem was introduced by Cook et al. in 2010 as a candidate for separating P from L and NL. The most general space lower bounds known for the Tree Evaluation Problem require a semantic restriction on the branching…
We study the arithmetic circuit complexity of some well-known family of polynomials through the lens of parameterized complexity. Our main focus is on the construction of explicit algebraic branching programs (ABP) for determinant and…
The aim of this paper is to highlight a hitherto unknown computational aspect of Nonstandard Analysis. Recently, a number of nonstandard versions of Goedel's system T have been introduced ([2,9,12]), and it was shown in [26] that the…
Large Language Models (LLMs) have achieved remarkable progress through Reinforcement Learning with Verifiable Rewards (RLVR), yet still rely heavily on external supervision (e.g., curated labels). Adversarial learning, particularly through…
Adversarial board games, as a paradigmatic domain of strategic reasoning and intelligence, have long served as both a popular competitive activity and a benchmark for evaluating artificial intelligence (AI) systems. Building on this…
The last decade has seen a revival of interest in pebble games in the context of proof complexity. Pebbling has proven a useful tool for studying resolution-based proof systems when comparing the strength of different subsystems, showing…
A recently introduced measure of Boolean functions complexity--disjunc\-tive complexity (DC)--is compared with other complexity measures: the space complexity of streaming algorithms and the complexity of nondeterministic branching programs…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed at combining statistical and logical knowledge representation and inference. A key…
In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of…
We show that assuming the Exponential Time Hypothesis, the Partial Minimum Branching Program Size Problem (MBPSP*) requires superpolynomial time. This result also applies to the partial minimization problems for many interesting subclasses…
This paper introduces a class of continuous-time, finite-player stochastic general-sum differential games that admit solutions through an exact linear PDE system. We formulate a distribution planning game utilizing the cross-log-likelihood…
This article presents a new game semantics for Martin-L\"of type theory (MLTT), in which each game is equipped with selected isomorphism strategies that represent (computational) proofs for (intensional) equality between strategies on the…