On The Complexity of Counter Reachability Games

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Fundamenta Informaticae Pub Date : 2013-07-18 DOI:10.3233/FI-2016-1320

J. Reichert

引用次数: 17

Abstract

Counter reachability games are played by two players on a graph with labelled edges. Each move consists in picking an edge from the current location and adding its label to a counter vector. The objective is to reach a given counter value in a given location. We distinguish three semantics for counter reachability games, according to what happens when a counter value would become negative: the edge is either disabled, or enabled but the counter value becomes zero, or enabled. We consider the problem of deciding the winner in counter reachability games and show that, in most cases, it has the same complexity under all semantics. Surprisingly, under one semantics, the complexity in dimension one depends on whether the objective value is zero or any other integer.

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论反可达性游戏的复杂性

计数器可达性博弈是由两名玩家在带有标记边缘的图上进行的。每次移动包括从当前位置选择一条边并将其标签添加到计数器向量。目标是在给定位置达到给定的计数器值。根据计数器值变为负值时的情况，我们区分了计数器可达性游戏的三种语义:边缘被禁用或启用，但计数器值变为零或启用。我们考虑了在反可达性博弈中决定赢家的问题，并证明在大多数情况下，它在所有语义下具有相同的复杂性。令人惊讶的是，在一种语义下，第一维的复杂度取决于目标值是零还是其他任何整数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fundamenta Informaticae 工程技术-计算机：软件工程

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

9.8 months

期刊介绍： Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing: solutions by mathematical methods of problems emerging in computer science solutions of mathematical problems inspired by computer science. Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, algebraic and categorical methods.