Deciding Determinism of Regular Languages

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	Deciding Determinism of Regular Languages
	Lu, Ping (1); Bremer, Joachim (2); Chen, Haiming (1); Lu, Ping
	2014
发表期刊	Theory of Computing Systems
ISSN	14324350
摘要	We investigate the problem to decide for DFAs, NFAs and regular expressions whether they describe deterministic regular languages. For DFAs with limited alphabet size we show the NL-completeness (nondeterministic logarithmic space-completeness) of the problem. Brüggemann-Klein and Wood (Inf. Comput. 142(2), 182–206, (1998)) gave an algorithm deciding for a minimal DFA whether it recognizes a deterministic regular language. Their algorithm requires polynomial time. Based on this algorithm we construct an algorithm for those DFAs which are not necessarily minimal, but limited in the size of the alphabet. We first focus on the case that the DFAs are minimal and extend to general DFAs later on. The new algorithm is substantially modified in contrast to the original one and uses structural properties of minimal DFAs and of special subautomata of the DFAs, called orbit automata. This algorithm runs in nondeterministic logarithmic space. After that we show the NL-hardness of the problem. For NFAs and regular expressions with arbitrary alphabets the problem is shown to be in PSPACE by Czerwiski et al. (2013) (and, in fact, to be PSPACE-complete). Their approach resulted in an algorithm working with space (Formula presented.). However, our approach for the NL-algorithm can be modified to get an algorithm for NFAs and regular expressions using just quadratic space.; We investigate the problem to decide for DFAs, NFAs and regular expressions whether they describe deterministic regular languages. For DFAs with limited alphabet size we show the NL-completeness (nondeterministic logarithmic space-completeness) of the problem. Brüggemann-Klein and Wood (Inf. Comput. 142(2), 182–206, (1998)) gave an algorithm deciding for a minimal DFA whether it recognizes a deterministic regular language. Their algorithm requires polynomial time. Based on this algorithm we construct an algorithm for those DFAs which are not necessarily minimal, but limited in the size of the alphabet. We first focus on the case that the DFAs are minimal and extend to general DFAs later on. The new algorithm is substantially modified in contrast to the original one and uses structural properties of minimal DFAs and of special subautomata of the DFAs, called orbit automata. This algorithm runs in nondeterministic logarithmic space. After that we show the NL-hardness of the problem. For NFAs and regular expressions with arbitrary alphabets the problem is shown to be in PSPACE by Czerwiski et al. (2013) (and, in fact, to be PSPACE-complete). Their approach resulted in an algorithm working with space (Formula presented.). However, our approach for the NL-algorithm can be modified to get an algorithm for NFAs and regular expressions using just quadratic space.
收录类别	EI
部门归属	(1) State Key Laboratory of Computer Science Institute of Software, Chinese Academy of Sciences, Beijing, China; (2) Institut fr Informatik, Goethe-Universitt, Frankfurt am Main, Germany
语种	英语
WOS记录号	WOS:000358741300004
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/17037
专题	中国科学院软件研究所
通讯作者	Lu, Ping
推荐引用方式 GB/T 7714	Lu, Ping ,Bremer, Joachim ,Chen, Haiming ,et al. Deciding Determinism of Regular Languages[J]. Theory of Computing Systems,2014.
APA	Lu, Ping ,Bremer, Joachim ,Chen, Haiming ,&Lu, Ping.(2014).Deciding Determinism of Regular Languages.Theory of Computing Systems.
MLA	Lu, Ping ,et al."Deciding Determinism of Regular Languages".Theory of Computing Systems (2014).