on the complexity of minimizing probabilistic and quantum automata

ISCAS OpenIR

	on the complexity of minimizing probabilistic and quantum automata
	Mateus Paulo; Qiu Daowen; Li Lvzhou
	2012
发表期刊	Information and Computation
ISSN	8905401
卷号	218 页码:36-53
摘要	Several types of automata, such as probabilistic and quantum automata, require to work with real and complex numbers. For such automata the acceptance of an input is quantified with a probability. There are plenty of results in the literature addressing the complexity of checking the equivalence of these automata, that is, checking whether two automata accept all inputs with the same probability. On the other hand, the critical problem of finding the minimal automata equivalent to a given one has been left open [C. Moore, J.P. Crutchfield, Quantum automata and quantum grammars, Theoret. Comput. Sci. 237 (2000) 275-306, see p. 304, Problem 5]. In this work, we reduce the minimization problem of probabilistic and quantum automata to finding a solution of a system of algebraic polynomial (in)equations. An EXPSPACE upper bound on the complexity of the minimization problem is derived by applying Renegars algorithm. More specifically, we show that the state minimization of probabilistic automata, measure-once quantum automata, measure-many quantum automata, measure-once generalized quantum automata, and measure-many generalized quantum automata is decidable and in EXPSPACE. Finally, we also solve an open problem concerning minimal covering of stochastic sequential machines [A. Paz, Introduction to Probabilistic Automata, Academic Press, New York, 1971, p. 43]. © 2012 Elsevier Inc.
收录类别	ei
部门归属	(1) SQIG, Instituto de Telecomunicações, Av. Rovisco Pais 1049-001, Lisbon, Portugal; (2) Dep. Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal; (3) Department of Computer Science, Sun Yat-sen University, Guangzhou 510006, China; (4) State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100080, China
语种	英语
WOS记录号	WOS:000309195100003
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/14728
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Mateus Paulo,Qiu Daowen,Li Lvzhou. on the complexity of minimizing probabilistic and quantum automata[J]. Information and Computation,2012,218:36-53.
APA	Mateus Paulo,Qiu Daowen,&Li Lvzhou.(2012).on the complexity of minimizing probabilistic and quantum automata.Information and Computation,218,36-53.
MLA	Mateus Paulo,et al."on the complexity of minimizing probabilistic and quantum automata".Information and Computation 218(2012):36-53.

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