Related papers: Classical realizability and arithmetical formul{\a…
In the lambda calculus a term is solvable iff it is operationally relevant. Solvable terms are a superset of the terms that convert to a final result called normal form. Unsolvable terms are operationally irrelevant and can be equated…
Example-based guidance is widely used to improve mathematical reasoning at inference time, yet its effectiveness is highly unstable across problems and models-even when the guidance is correct and problem-relevant. We show that this…
A rational number can be naturally presented by an arithmetic computation (AC): a sequence of elementary arithmetic operations starting from a fixed constant, say 1. The asymptotic complexity issues of such a representation are studied e.g.…
We propose a unifying additive theory for standard conventions in Combinatorial Game Theory, including normal-, mis\`ere- and scoring-play, studied by Berlekamp, Conway, Dorbec, Ettinger, Guy, Larsson, Milley, Neto, Nowakowski, Renault,…
Program synthesis is the task of automatically deriving a program that has been specified by a user in advance. Combining automated theorem proving with program synthesis enables the automated construction of proven-to-be-correct programs,…
We study approachability theory in the presence of constraints. Given a repeated game with vector payoffs, we characterize the pairs of sets (A,D) in the payoff space such that Player 1 can guarantee that the long-run average payoff…
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…
We extend the classical notion of solvability to a lambda-calculus equipped with pattern matching. We prove that solvability can be characterized by means of typability and inhabitation in an intersection type system P based on…
We study two player reachability-price games on single-clock timed automata. The problem is as follows: given a state of the automaton, determine whether the first player can guarantee reaching one of the designated goal locations. If a…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
Linearizability is a commonly accepted notion of correctness for libraries of concurrent algorithms, and recent years have seen a number of proposals of program logics for proving it. Although these logics differ in technical details, they…
We examine the interplay between projectivity (in the sense that was introduced by S.~Ghilardi) and uniform post-interpolant for the classical and intuitionistic propositional logic. More precisely, we explore whether a projective…
We consider two-player games with imperfect information and the synthesis of a randomized strategy for one player that ensures the objective is satisfied almost-surely (i.e., with probability 1), regardless of the strategy of the other…
The parameterized complexity of a problem is considered "settled" once it has been shown to lie in FPT or to be complete for a class in the W-hierarchy or a similar parameterized hierarchy. Several natural parameterized problems have,…
In this paper we introduce the reactivity in decision-form games. The concept of reactivity allows us to give a natural concept of rationalizable solution for decision-form games: the solubility by elimination of sub-reactive strategies.…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Extensive-form games constitute the standard representation scheme for games with a temporal component. But do all extensive-form games correspond to protocols that we can implement in the real world? We often rule out games with imperfect…
In this paper, we address the problem of the (reactive) realizability of specifications of theories richer than Booleans, including arithmetic theories. Our approach transforms theory specifications into purely Boolean specifications by (1)…
A Bayesian player acting in an infinite multi-player game learns to predict the other players' strategies if his prior assigns positive probability to their play (or contains a grain of truth). Kalai and Lehrer's classic grain of truth…
This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a…