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Automata theory based on lattice-ordered semirings
Lu, Xian; Shang, Yun; Lu, Ruqian
Source PublicationSOFT COMPUTING
AbstractIn this paper, definitions of K automata, K regular languages, K regular expressions and K regular grammars based on lattice-ordered semirings are given. It is shown that KNFA is equivalent to KDFA under some finite condition, the Pump Lemma holds if K is finite, and K epsilon NFA is equivalent to KNFA. Further, it is verified that the concatenation of K regular languages remains a K regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that KNFA, K regular expressions and K regular grammars are equivalent to each other when K is a complete lattice.
KeywordLattice-ordered semirings K automata K regular languages K regular expressions K regular grammars
Funding ProjectNSFC[60496324] ; NSFC[6002530760234010] ; NSFC[60603002] ; Pre-973 Project[2001CCA03000] ; 863 High-Tech Project[2001AA113130] ; 973 Project[2001CB312004] ; CAS Brain and Mind Science Project ; China Postdoctoral Science Foundation
WOS Research AreaComputer Science
WOS SubjectComputer Science, Artificial Intelligence ; Computer Science, Interdisciplinary Applications
WOS IDWOS:000287593200006
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Document Type期刊论文
Corresponding AuthorShang, Yun
AffiliationAcad Mil Med Sci, Acad Sinica, Inst Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Lu, Xian,Shang, Yun,Lu, Ruqian. Automata theory based on lattice-ordered semirings[J]. SOFT COMPUTING,2011,15(2):269-280.
APA Lu, Xian,Shang, Yun,&Lu, Ruqian.(2011).Automata theory based on lattice-ordered semirings.SOFT COMPUTING,15(2),269-280.
MLA Lu, Xian,et al."Automata theory based on lattice-ordered semirings".SOFT COMPUTING 15.2(2011):269-280.
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