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Title:
Deciding determinism of unary languages
Author: Lu, P ; Peng, FF ; Chen, HM ; Zheng, LX
Keyword: Regular expressions ; Regular expressions with counting ; Deterministic languages ; Minimal DFA ; coNP-complete ; Pi(p)(2)
Source: INFORMATION AND COMPUTATION
Issued Date: 2015
Volume: 245, Pages:181-196
Indexed Type: SCI
Department: Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100190, Peoples R China. Chinese Acad Sci, Grad Univ, Beijing 100190, Peoples R China. Univ Chinese Acad Sci, Beijing, Peoples R China. Huaqiao Univ, Coll Comp Sci & Technol, Xiamen 361021, Fujian, Peoples R China.
Abstract: In this paper, we investigate the complexity of deciding determinism of unary languages. First, we give a method to derive a set of arithmetic progressions from a regular expression Eover a unary alphabet, and establish relations between numbers represented by these arithmetic progressions and words in L( E). Next, we define a problem relating to arithmetic progressions and investigate the complexity of this problem. Then by a reduction from this problem we show that deciding determinism of unary languages iscoNPcomplete. Finally, we extend our derivation method to expressions with counting, and prove that deciding whether an expression over a unary alphabet with counting defines a deterministic language is in Pi(p)(2). We also establish a tight upper bound for the size of the minimal DFA for expressions with counting. (C) 2015 Elsevier Inc. Allrightsreserved.
English Abstract: In this paper, we investigate the complexity of deciding determinism of unary languages. First, we give a method to derive a set of arithmetic progressions from a regular expression Eover a unary alphabet, and establish relations between numbers represented by these arithmetic progressions and words in L( E). Next, we define a problem relating to arithmetic progressions and investigate the complexity of this problem. Then by a reduction from this problem we show that deciding determinism of unary languages iscoNPcomplete. Finally, we extend our derivation method to expressions with counting, and prove that deciding whether an expression over a unary alphabet with counting defines a deterministic language is in Pi(p)(2). We also establish a tight upper bound for the size of the minimal DFA for expressions with counting. (C) 2015 Elsevier Inc. Allrightsreserved.
Language: 英语
WOS ID: WOS:000368899100012
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/17428
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Lu, P,Peng, FF,Chen, HM,et al. Deciding determinism of unary languages[J]. INFORMATION AND COMPUTATION,2015-01-01,245:181-196.
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