Related papers: Local obstructions in sequences revisited
Finite turn-based safety games have been used for very different problems such as the synthesis of linear temporal logic (LTL), the synthesis of schedulers for computer systems running on multiprocessor platforms, and also for the…
We study the computational complexity of the popular board game backgammon. We show that deciding whether a player can win from a given board configuration is NP-Hard, PSPACE-Hard, and EXPTIME-Hard under different settings of known and…
The goal of this article is to understand some interesting features of sequences of arbitrage operations, which look relevant to various processes in Economics and Finances. In the second part of the paper, analysis of sequences of…
Competition among cooperators, defectors, and loners is studied in an evolutionary prisoner's dilemma game with optional participation. Loners are risk averse i.e. unwilling to participate and rather rely on small but fixed earnings. This…
Capacitated network bargaining games are popular combinatorial games that involve the structure of matchings in graphs. We show that it is always possible to stabilize unit-weight instances of this problem (that is, ensure that they admit a…
Fictitious play with reinforcement learning is a general and effective framework for zero-sum games. However, using the current deep neural network models, the implementation of fictitious play faces crucial challenges. Neural network model…
The brain is targeted for processing temporal sequence information. It remains largely unclear how the brain learns to store and retrieve sequence memories. Here, we study how recurrent networks of binary neurons learn sequence attractors…
Combinatorial games are two-player games of pure strategy where the players, usually called Left and Right, move alternately. In this paper, we introduce Cheating Robot games. These arise from simultaneous-play combinatorial games where one…
This text provides an introduction to distributed local algorithms -- an area at the intersection of theoretical computer science and discrete mathematics. We collect recent results in the area and demonstrate how they lead to a clean…
Suppose that the outcomes of a roulette table are not entirely random, in the sense that there exists a successful betting strategy. Is there a successful `separable' strategy, in the sense that it does not use the winnings from betting on…
This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the…
The generalization of the problem of adaptive competition, known as the minority game, to the case of $K$ possible choices for each player is addressed, and applied to a system of interacting perceptrons with input and output units of the…
We investigate certain word-construction games with variable turn orders. In these games, Alice and Bob take turns on choosing consecutive letters of a word of fixed length, with Alice winning if the result lies in a predetermined target…
We study two-player games played on the infinite graph of sentential forms induced by a context-free grammar (that comes with an ownership partitioning of the non-terminals). The winning condition is inclusion of the derived terminal word…
In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed as a disjunctive sum of two forms with smaller birthday. If…
Let S be a topological property of sequences (such as, for example, "to contain a convergent subsequence" or "to have an accumulation point"). We introduce the following open-point game OP(X,S) on a topological space X. In the n'th move,…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
We propose a simple method for combining together voting rules that performs a run-off between the different winners of each voting rule. We prove that this combinator has several good properties. For instance, even if just one of the base…
A knockout tournament is one of the most simple and popular forms of competition. Here, we are given a binary tournament tree where all leaves are labeled with seed position names. The players participating in the tournament are assigned to…
We study the problem of learning a good search policy for combinatorial search spaces. We propose retrospective imitation learning, which, after initial training by an expert, improves itself by learning from \textit{retrospective…