Related papers: Local obstructions in sequences revisited
In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…
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.…
Motivated by the "tug-of-war" game studied in [12], we consider a "non-local" version of the game which goes as follows: at every step two players pick respectively a direction and then, instead of flipping a coin in order to decide which…
Poker is a family of card games that includes many variations. We hypothesize that most poker games can be solved as a pattern matching problem, and propose creating a strong poker playing system based on a unified poker representation. Our…
Positional games are a well-studied class of combinatorial game. In their usual form, two players take turns to play moves in a set (`the board'), and certain subsets are designated as `winning': the first person to occupy such a set wins…
We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…
The ability of a deterministic, plastic system to learn to imitate stochastic behavior is analyzed. Two neural networks -actually, two perceptrons- are put to play a zero-sum game one against the other. The competition, by acting as a kind…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play $\omega$ many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
Recurrent Neural Network, Long Short-Term Memory, and Transformer have made great progress in predicting the trajectories of moving objects. Although the trajectory element with the surrounding scene features has been merged to improve…
The following problem is considered. Two players are each required to allocate a quota of~$n$ counters among~$k$ boxes labelled~$1,2,\ldots,k$. At times $t=1,2,3,\ldots$ a random box is identified; the probability of choosing box~$i$…
Inspired by the efficient proof procedures discussed in {\em Computability logic} \cite{Jap03,Japic,Japfin}, we describe a heuristic proof procedure for first-order logic. This is a variant of Gentzen sequent system and has the following…
We study a pursuit-evasion problem which can be viewed as an extension of the keep-away game. In the game, pursuer(s) will attempt to intersect or catch the evader, while the evader can visit a fixed set of locations, which we denote as the…
Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of…
We develop the novel machinery of smooth approximations, and apply it to confirm the CSP dichotomy conjecture for first-order reducts of the random tournament, various homogeneous graphs including the random graph, and for expansions of the…
We present a general theorem for distributed synthesis problems in coordination games with $\omega$-regular objectives of the form: If there exists a winning strategy for the coalition, then there exists an "essential" winning strategy,…
This letter employs differential game theory to address the defense problem of a circular target area with perception constraints, involving a single defender and a single attacker. The defender is restricted to moving along the perimeter,…
We consider the permutation analogue of Penney's game for words. Two players, in order, each choose a permutation of length $k\ge3$; then a sequence of independent random values from a continuous distribution is generated, until the…
Many classification problems require decisions among a large number of competing classes. These tasks, however, are not handled well by general purpose learning methods and are usually addressed in an ad-hoc fashion. We suggest a general…