Related papers: Perron transforms and Hironaka's game
The strategy improvement algorithm for mean payoff games and parity games is a local improvement algorithm, just like the simplex algorithm for linear programs. Their similarity has turned out very useful: many lower bounds on running time…
Transformer networks have seen great success in natural language processing and machine vision, where task objectives such as next word prediction and image classification benefit from nuanced context sensitivity across high-dimensional…
This paper investigates the popular card game UNO from the viewpoint of algorithmic combinatorial game theory. We define simple and concise mathematical models for the game, including both cooperative and uncooperative versions, and analyze…
In this article we prove the existence of classical solutions to a system of mean field games arising in the study of exhaustible resource production under market competition. Individual trajectories are modeled by a controlled diffusion…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
The Perron-Frobenius theorem plays an important role in many areas of management science and operations research. This paper provides a probabilistic perspective on the theorem, by discussing a proof that exploits a probabilistic…
Parrondo's paradox arises in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. We present a suitable version…
In this paper, by using permutation matrices as a representation of symmetric group $S_N$ and Fourier matrix, we investigate quantum roulette with an arbitrary $N$-state. This strategy, which we introduce, is general method that allows us…
We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant…
Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…
In this note we prove the uniqueness of solutions to a class of Mean Field Games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general non-separable Hamiltonians that…
Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different…
We prove that several results in different areas of number theory such as the divergent series, summation of arithmetic functions, uniform distribution modulo one and summation over prime numbers which are currently considered to be…
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…
The paper is devoted to the methods of solving simultaneous recurrences. Specifically, we discuss transformation of matrix recurrences to regular recurrences and propose a way of solving special matrix recurrences of order three by their…
Machine learning presents a general, systematic framework for the generation of formal theoretical models for physical description and prediction. Tentatively standard linear modeling techniques are reviewed; followed by a brief discussion…
A zero-one matrix $A$ contains another zero-one matrix $P$ if some submatrix of $A$ can be transformed to $P$ by changing some ones to zeros. $A$ avoids $P$ if $A$ does not contain $P$. The Pattern Avoidance Game is played by two players.…
We present a combinatorial game and propose efficiently computable optimal strategies. We then show how these strategies can be translated to efficiently computable shift-rules for the well known prefer-max and prefer-min De Bruijn…
In this paper, we further investigate the local criterion and present a class of permutation polynomials and their compositional inverses over $ \mathbb{F}_{q^2}$. Additionally, we demonstrate that linearized polynomial over…
We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…