On Almost-Sure Properties of Probabilistic Discrete Event Systems

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING Fundamenta Informaticae Pub Date : 2010-01-01 DOI:10.3233/FI-2011-548
H. Yen
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Abstract

Although randomization often increases the degree of flexibility in system design, analyzing system properties in the probabilistic framework introduces additional difficulties and challenges in comparison with their nonprobabilistic counterparts. In this paper, we focus on probabilistic versions of two problems frequently encountered in discrete event systems, namely, the reachability and forbidden-state problems. Our main concern is to see whether there exists a (or for every) non-blocking or fair control policy under which a given finite- or infinite-state system can be guided to reach (or avoid) a set of goal states with probability one. For finite-state systems, we devise algorithmic approaches which result in polynomial time solutions to the two problems. For infinite-state systems modelled as Petri nets, the problems are undecidable in general. For the class of persistent Petri nets, we establish a valuation approach through which the convergence behavior of a system is characterized, which in turn yields solutions to the reachability and forbidden-state problems.
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关于概率离散事件系统的几乎确定性质
尽管随机化通常会增加系统设计的灵活性,但与非概率框架相比,在概率框架中分析系统属性会带来额外的困难和挑战。本文主要研究离散事件系统中两个常见问题的概率问题,即可达性问题和禁止状态问题。我们主要关注的是是否存在一个(或每一个)无阻塞或公平的控制策略,在该策略下,给定的有限或无限状态系统可以被引导以概率1达到(或避免)一组目标状态。对于有限状态系统,我们设计了算法方法,可以在多项式时间内解决这两个问题。对于用Petri网建模的无限状态系统,问题通常是不可确定的。对于一类持久Petri网,我们建立了一种评估方法,通过该方法表征系统的收敛行为,从而得到可达性和禁止状态问题的解。
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来源期刊
Fundamenta Informaticae
Fundamenta Informaticae 工程技术-计算机:软件工程
CiteScore
2.00
自引率
0.00%
发文量
61
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.
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