Automata theory based on lattice-ordered semirings
Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$D...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Lu, Xian [verfasserIn] Shang, Yun [verfasserIn] Lu, Ruqian [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2010 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Soft Computing - Springer-Verlag, 2003, 15(2010), 2 vom: 10. März, Seite 269-280 |
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| Übergeordnetes Werk: |
volume:15 ; year:2010 ; number:2 ; day:10 ; month:03 ; pages:269-280 |
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| DOI / URN: |
10.1007/s00500-010-0565-3 |
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| 520 | |a Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$DFA under some finite condition, the Pump Lemma holds if %${\mathcal{K}}%$ is finite, and %${{\mathcal{K}}}\epsilon%$NFA is equivalent to %${\mathcal{K}}%$NFA. Further, it is verified that the concatenation of %${\mathcal{K}}%$ regular languages remains a %${\mathcal{K}}%$ regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that %${\mathcal{K}}%$NFA, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars are equivalent to each other when %${\mathcal{K}}%$ is a complete lattice. | ||
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| 700 | 1 | |a Lu, Ruqian |e verfasserin |4 aut | |
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10.1007/s00500-010-0565-3 doi (DE-627)SPR006478476 (SPR)s00500-010-0565-3-e DE-627 ger DE-627 rakwb eng Lu, Xian verfasserin aut Automata theory based on lattice-ordered semirings 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$DFA under some finite condition, the Pump Lemma holds if %${\mathcal{K}}%$ is finite, and %${{\mathcal{K}}}\epsilon%$NFA is equivalent to %${\mathcal{K}}%$NFA. Further, it is verified that the concatenation of %${\mathcal{K}}%$ regular languages remains a %${\mathcal{K}}%$ regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that %${\mathcal{K}}%$NFA, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars are equivalent to each other when %${\mathcal{K}}%$ is a complete lattice. Lattice-ordered semirings (dpeaa)DE-He213 automata (dpeaa)DE-He213 regular languages (dpeaa)DE-He213 regular expressions (dpeaa)DE-He213 regular grammars (dpeaa)DE-He213 Shang, Yun verfasserin aut Lu, Ruqian verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 15(2010), 2 vom: 10. März, Seite 269-280 (DE-627)SPR006469531 nnns volume:15 year:2010 number:2 day:10 month:03 pages:269-280 https://dx.doi.org/10.1007/s00500-010-0565-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 15 2010 2 10 03 269-280 |
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10.1007/s00500-010-0565-3 doi (DE-627)SPR006478476 (SPR)s00500-010-0565-3-e DE-627 ger DE-627 rakwb eng Lu, Xian verfasserin aut Automata theory based on lattice-ordered semirings 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$DFA under some finite condition, the Pump Lemma holds if %${\mathcal{K}}%$ is finite, and %${{\mathcal{K}}}\epsilon%$NFA is equivalent to %${\mathcal{K}}%$NFA. Further, it is verified that the concatenation of %${\mathcal{K}}%$ regular languages remains a %${\mathcal{K}}%$ regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that %${\mathcal{K}}%$NFA, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars are equivalent to each other when %${\mathcal{K}}%$ is a complete lattice. Lattice-ordered semirings (dpeaa)DE-He213 automata (dpeaa)DE-He213 regular languages (dpeaa)DE-He213 regular expressions (dpeaa)DE-He213 regular grammars (dpeaa)DE-He213 Shang, Yun verfasserin aut Lu, Ruqian verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 15(2010), 2 vom: 10. März, Seite 269-280 (DE-627)SPR006469531 nnns volume:15 year:2010 number:2 day:10 month:03 pages:269-280 https://dx.doi.org/10.1007/s00500-010-0565-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 15 2010 2 10 03 269-280 |
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10.1007/s00500-010-0565-3 doi (DE-627)SPR006478476 (SPR)s00500-010-0565-3-e DE-627 ger DE-627 rakwb eng Lu, Xian verfasserin aut Automata theory based on lattice-ordered semirings 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$DFA under some finite condition, the Pump Lemma holds if %${\mathcal{K}}%$ is finite, and %${{\mathcal{K}}}\epsilon%$NFA is equivalent to %${\mathcal{K}}%$NFA. Further, it is verified that the concatenation of %${\mathcal{K}}%$ regular languages remains a %${\mathcal{K}}%$ regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that %${\mathcal{K}}%$NFA, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars are equivalent to each other when %${\mathcal{K}}%$ is a complete lattice. Lattice-ordered semirings (dpeaa)DE-He213 automata (dpeaa)DE-He213 regular languages (dpeaa)DE-He213 regular expressions (dpeaa)DE-He213 regular grammars (dpeaa)DE-He213 Shang, Yun verfasserin aut Lu, Ruqian verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 15(2010), 2 vom: 10. März, Seite 269-280 (DE-627)SPR006469531 nnns volume:15 year:2010 number:2 day:10 month:03 pages:269-280 https://dx.doi.org/10.1007/s00500-010-0565-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 15 2010 2 10 03 269-280 |
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10.1007/s00500-010-0565-3 doi (DE-627)SPR006478476 (SPR)s00500-010-0565-3-e DE-627 ger DE-627 rakwb eng Lu, Xian verfasserin aut Automata theory based on lattice-ordered semirings 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$DFA under some finite condition, the Pump Lemma holds if %${\mathcal{K}}%$ is finite, and %${{\mathcal{K}}}\epsilon%$NFA is equivalent to %${\mathcal{K}}%$NFA. Further, it is verified that the concatenation of %${\mathcal{K}}%$ regular languages remains a %${\mathcal{K}}%$ regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that %${\mathcal{K}}%$NFA, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars are equivalent to each other when %${\mathcal{K}}%$ is a complete lattice. Lattice-ordered semirings (dpeaa)DE-He213 automata (dpeaa)DE-He213 regular languages (dpeaa)DE-He213 regular expressions (dpeaa)DE-He213 regular grammars (dpeaa)DE-He213 Shang, Yun verfasserin aut Lu, Ruqian verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 15(2010), 2 vom: 10. März, Seite 269-280 (DE-627)SPR006469531 nnns volume:15 year:2010 number:2 day:10 month:03 pages:269-280 https://dx.doi.org/10.1007/s00500-010-0565-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 15 2010 2 10 03 269-280 |
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10.1007/s00500-010-0565-3 doi (DE-627)SPR006478476 (SPR)s00500-010-0565-3-e DE-627 ger DE-627 rakwb eng Lu, Xian verfasserin aut Automata theory based on lattice-ordered semirings 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$DFA under some finite condition, the Pump Lemma holds if %${\mathcal{K}}%$ is finite, and %${{\mathcal{K}}}\epsilon%$NFA is equivalent to %${\mathcal{K}}%$NFA. Further, it is verified that the concatenation of %${\mathcal{K}}%$ regular languages remains a %${\mathcal{K}}%$ regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that %${\mathcal{K}}%$NFA, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars are equivalent to each other when %${\mathcal{K}}%$ is a complete lattice. Lattice-ordered semirings (dpeaa)DE-He213 automata (dpeaa)DE-He213 regular languages (dpeaa)DE-He213 regular expressions (dpeaa)DE-He213 regular grammars (dpeaa)DE-He213 Shang, Yun verfasserin aut Lu, Ruqian verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 15(2010), 2 vom: 10. März, Seite 269-280 (DE-627)SPR006469531 nnns volume:15 year:2010 number:2 day:10 month:03 pages:269-280 https://dx.doi.org/10.1007/s00500-010-0565-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 15 2010 2 10 03 269-280 |
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Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$DFA under some finite condition, the Pump Lemma holds if %${\mathcal{K}}%$ is finite, and %${{\mathcal{K}}}\epsilon%$NFA is equivalent to %${\mathcal{K}}%$NFA. Further, it is verified that the concatenation of %${\mathcal{K}}%$ regular languages remains a %${\mathcal{K}}%$ regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that %${\mathcal{K}}%$NFA, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars are equivalent to each other when %${\mathcal{K}}%$ is a complete lattice. |
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Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$DFA under some finite condition, the Pump Lemma holds if %${\mathcal{K}}%$ is finite, and %${{\mathcal{K}}}\epsilon%$NFA is equivalent to %${\mathcal{K}}%$NFA. Further, it is verified that the concatenation of %${\mathcal{K}}%$ regular languages remains a %${\mathcal{K}}%$ regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that %${\mathcal{K}}%$NFA, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars are equivalent to each other when %${\mathcal{K}}%$ is a complete lattice. |
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Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$DFA under some finite condition, the Pump Lemma holds if %${\mathcal{K}}%$ is finite, and %${{\mathcal{K}}}\epsilon%$NFA is equivalent to %${\mathcal{K}}%$NFA. Further, it is verified that the concatenation of %${\mathcal{K}}%$ regular languages remains a %${\mathcal{K}}%$ regular language. Similar to classical cases and automata theory based on lattice-ordered monoids, it is also found that %${\mathcal{K}}%$NFA, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars are equivalent to each other when %${\mathcal{K}}%$ is a complete lattice. |
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10.1007/s00500-010-0565-3 |
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2024-07-03T23:13:36.430Z |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR006478476</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20201124002731.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2010 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00500-010-0565-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR006478476</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00500-010-0565-3-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lu, Xian</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Automata theory based on lattice-ordered semirings</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2010</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, definitions of %${\mathcal{K}}%$ automata, %${\mathcal{K}}%$ regular languages, %${\mathcal{K}}%$ regular expressions and %${\mathcal{K}}%$ regular grammars based on lattice-ordered semirings are given. It is shown that %${\mathcal{K}}%$NFA is equivalent to %${\mathcal{K}}%$DFA under some finite condition, the Pump Lemma holds if %${\mathcal{K}}%$ is finite, and %${{\mathcal{K}}}\epsilon%$NFA is equivalent to %${\mathcal{K}}%$NFA. Further, it is verified that the concatenation of %${\mathcal{K}}%$ regular languages remains a %${\mathcal{K}}%$ regular language. 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