Related papers: Decidability of higher-order matching
We solve the classical "Game of Pure Strategy" using linear programming. We notice an intricate even-odd behavior in the results of our computations, that seems to encourage odd or maximal bids.
Linearisability is a central notion for verifying concurrent libraries: a given library is proven safe if its operational history can be rearranged into a new sequential one which, in addition, satisfies a given specification.…
We show that the first-order logical theory of the binary overlap-free words (and, more generally, the ${\alpha}$-free words for rational ${\alpha}$, $2 < {\alpha} \leq 7/3$), is decidable. As a consequence, many results previously obtained…
We prove that the following problem is decidable: given a finite set of relations, decide whether this set admits a near-unanimity function.
A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidability of the diagonal problem for schemes. This…
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…
Higher-order beta-matching is the following decision problem: given two simply typed lambda-terms, can the first term be instantiated to be beta-equivalent to the second term? This problem was formulated by Huet in the 1970s and shown…
Higher-order interactions are prevalent in real-world complex systems and exert unique influences on system evolution that cannot be captured by pairwise interactions. We incorporate game transitions into the higher-order prisoner's dilemma…
Using the technique of formative processes, I solve the decidability problem of MLS with unordered cartesian product in the positive. Moreover I give a pure combinatorial description of the satisfiable MLS with unordered cartesian…
We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…
The logic of the hide and seek game LHS was proposed to reason about search missions and interactions between agents in pursuit-evasion environments. As proved in literature, having an equality constant in the language of LHS drastically…
Infinite chess is chess played on an infinite edgeless chessboard. The familiar chess pieces move about according to their usual chess rules, and each player strives to place the opposing king into checkmate. The mate-in-n problem of…
The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient…
We prove two determinacy and decidability results about two-players stochastic reachability games with partial observation on both sides and finitely many states, signals and actions.
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
We study two-player games with alternating moves played on infinite trees. Our main focus is on the case where the trees are full (regular) and the winning set is open (with respect to the product topology on the tree). Gale and Stewart…
As the widely applied method for measuring matching assortativeness in a transferable utility matching game, a matching maximum score estimation is proposed by \cite{fox2010qe}. This article reveals that combining unmatched agents,…
The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous…
A polynomial algorithm is obtained for the NP-complete linear ordering problem.
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…