Related papers: A Weak Solution of Inverse Treblecross

In this paper, we first formalize the problem to be solved, i.e., the Scatter Problem (SP). We then show that SP cannot be deterministically solved. Next, we propose a randomized algorithm for this problem. The proposed solution is…

The main of this work is to use the unit lower triangular matrices for solving inverse eigenvalue problem of nonnegative matrices and present the easier method to solve this problem.

In this paper we study a two person zero sum stochastic differential game in weak formulation. Unlike standard literature which uses strategy type of controls, the weak formulation allows us to consider the game with control against…

A finite impartial game is a two-player game in which the players take turns making moves and the game ends after finitely many moves. In this paper, we study a class of finite impartial games introduced by H.~Lenstra, which we call coin…

We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but…

Circular Nim is a two-player impartial combinatorial game consisting of $n$ stacks of tokens placed in a circle. A move consists of choosing $k$ consecutive stacks and taking at least one token from one or more of the stacks. The last…

An introduction and overview of constructive reverse mathematics.

We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…

We present a well-posedness and stability result for a class of nondegenerate linear parabolic equations driven by rough paths. More precisely, we introduce a notion of weak solution that satisfies an intrinsic formulation of the equation…

In this paper, we investigate the existence and characterization of the value for a two-player zero-sum differential game with symmetric incomplete information on a continuum of initial positions and with signal revelation. Before the game…

Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…

In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…

Limited lookahead has been studied for decades in perfect-information games. We initiate a new direction via two simultaneous deviation points: generalization to imperfect-information games and a game-theoretic approach. We study how one…

The space of finite games can be decomposed into three orthogonal subspaces [5], which are the subspaces of pure potential games, nonstrategic games and pure harmonic games. The orthogonal projections onto these subspaces are represented as…

A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the…

We propose a variant of Nim, named StrNim. Whereas a position in Nim is a tuple of non-negative integers, that in StrNim is a string, a sequence of characters. In every turn, each player shrinks the string, by removing a substring repeating…

A positional game is a game where two players sequentially label vertices of a hypergraph, consisting of a board and a collection of winning sets, with colors assigned to each player until all vertices of the board are claimed. The first…

A combinatorial game is a two-player game without hidden information or chance elements. The main object of combinatorial game theory is to obtain the outcome, which player has a winning strategy, of a given combinatorial game. Positions of…

We present the first game characterization of contrasimilarity, the weakest form of bisimilarity. The game is finite for finite-state processes and can thus be used for contrasimulation equivalence checking, of which no tool has been…

We introduce a class of "inverse parametric optimization" problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We…