A logical approach to locality in pictures languages
This paper deals with descriptive complexity of picture languages of any dimension by fragments of existential second-order logic: 1) We generalize to any dimension the characterization by Giammarresi et al. (1996) of the class of recognizable picture languages in existential monadic second-order lo...
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| Veröffentlicht in: | Journal of computer and system sciences 2016-09, Vol.82 (6), p.959-1006 |
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| container_title | Journal of computer and system sciences |
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| creator | Grandjean, Etienne Olive, Frédéric |
| description | This paper deals with descriptive complexity of picture languages of any dimension by fragments of existential second-order logic:
1) We generalize to any dimension the characterization by Giammarresi et al. (1996) of the class of recognizable picture languages in existential monadic second-order logic.
2) We state natural logical characterizations of the class of picture languages of any dimension d≥1 recognized in linear time on nondeterministic cellular automata, a robust complexity class that contains, for d=1, all the natural NP-complete problems.
Our characterizations are essentially deduced from normalization results for first-order and existential second-order logics over pictures.
•The class of recognizable picture languages is characterized by existential monadic second-order logic.•Logical characterizations of the class of picture languages recognized in linear time on nondeterministic cellular automata.•This shows the logics involved can be made “local” with respect to the underlying regular structures.•Hierarchy results among some logical frameworks are deduced from the above. |
| doi_str_mv | 10.1016/j.jcss.2016.01.005 |
| format | Article |
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1) We generalize to any dimension the characterization by Giammarresi et al. (1996) of the class of recognizable picture languages in existential monadic second-order logic.
2) We state natural logical characterizations of the class of picture languages of any dimension d≥1 recognized in linear time on nondeterministic cellular automata, a robust complexity class that contains, for d=1, all the natural NP-complete problems.
Our characterizations are essentially deduced from normalization results for first-order and existential second-order logics over pictures.
•The class of recognizable picture languages is characterized by existential monadic second-order logic.•Logical characterizations of the class of picture languages recognized in linear time on nondeterministic cellular automata.•This shows the logics involved can be made “local” with respect to the underlying regular structures.•Hierarchy results among some logical frameworks are deduced from the above.</description><identifier>ISSN: 0022-0000</identifier><identifier>EISSN: 1090-2724</identifier><identifier>DOI: 10.1016/j.jcss.2016.01.005</identifier><language>eng</language><publisher>Elsevier Inc</publisher><subject>Cellular automata ; Complexity ; Computational Complexity ; Computer Science ; Existential second-order logic ; Fragments ; Languages ; Linear time ; Locality and tiling ; Logic ; Logical characterizations ; Monadic second-order logic ; Picture languages ; Pictures ; Recognizability</subject><ispartof>Journal of computer and system sciences, 2016-09, Vol.82 (6), p.959-1006</ispartof><rights>2016 Elsevier Inc.</rights><rights>Copyright</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c481t-5e4f9924e78a030364c99a4c8bfb1a26e526c6f89e2447883dc9d7b02ca7bcc93</citedby><cites>FETCH-LOGICAL-c481t-5e4f9924e78a030364c99a4c8bfb1a26e526c6f89e2447883dc9d7b02ca7bcc93</cites><orcidid>0000-0002-3552-5566</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0022000016000258$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,776,780,881,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttps://hal.science/hal-00786148$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Grandjean, Etienne</creatorcontrib><creatorcontrib>Olive, Frédéric</creatorcontrib><title>A logical approach to locality in pictures languages</title><title>Journal of computer and system sciences</title><description>This paper deals with descriptive complexity of picture languages of any dimension by fragments of existential second-order logic:
1) We generalize to any dimension the characterization by Giammarresi et al. (1996) of the class of recognizable picture languages in existential monadic second-order logic.
2) We state natural logical characterizations of the class of picture languages of any dimension d≥1 recognized in linear time on nondeterministic cellular automata, a robust complexity class that contains, for d=1, all the natural NP-complete problems.
Our characterizations are essentially deduced from normalization results for first-order and existential second-order logics over pictures.
•The class of recognizable picture languages is characterized by existential monadic second-order logic.•Logical characterizations of the class of picture languages recognized in linear time on nondeterministic cellular automata.•This shows the logics involved can be made “local” with respect to the underlying regular structures.•Hierarchy results among some logical frameworks are deduced from the above.</description><subject>Cellular automata</subject><subject>Complexity</subject><subject>Computational Complexity</subject><subject>Computer Science</subject><subject>Existential second-order logic</subject><subject>Fragments</subject><subject>Languages</subject><subject>Linear time</subject><subject>Locality and tiling</subject><subject>Logic</subject><subject>Logical characterizations</subject><subject>Monadic second-order logic</subject><subject>Picture languages</subject><subject>Pictures</subject><subject>Recognizability</subject><issn>0022-0000</issn><issn>1090-2724</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9ULFOwzAQtRBIlMIPMGWEIeHsOIktsVQVUKRKLDBbzsVpHaVNsJNK_XscBTFyy52e3ru79wi5p5BQoPlTkzTofcLCnABNALILsqAgIWYF45dkAcBYDKGuyY33DQClWZ4uCF9FbbezqNtI973rNO6joQtYQOxwjuwx6i0OozM-avVxN-qd8bfkqtatN3e_fUm-Xl8-15t4-_H2vl5tY-SCDnFmeC0l46YQGlJIc45Sao6irEuqWW4ylmNeC2kY54UQaYWyKkpgqIsSUaZL8jjv3etW9c4etDurTlu1WW3VhAEUIqdcnGjgPszcYOJ7NH5QB-vRtOFp041eUcGyjKeSpoHKZiq6zntn6r_dFNQUp2rUFKea4lRAw5ksiJ5nkQmGT9Y45dGaI5rKOoODqjr7n_wHMqx8Pw</recordid><startdate>201609</startdate><enddate>201609</enddate><creator>Grandjean, Etienne</creator><creator>Olive, Frédéric</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0002-3552-5566</orcidid></search><sort><creationdate>201609</creationdate><title>A logical approach to locality in pictures languages</title><author>Grandjean, Etienne ; Olive, Frédéric</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c481t-5e4f9924e78a030364c99a4c8bfb1a26e526c6f89e2447883dc9d7b02ca7bcc93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Cellular automata</topic><topic>Complexity</topic><topic>Computational Complexity</topic><topic>Computer Science</topic><topic>Existential second-order logic</topic><topic>Fragments</topic><topic>Languages</topic><topic>Linear time</topic><topic>Locality and tiling</topic><topic>Logic</topic><topic>Logical characterizations</topic><topic>Monadic second-order logic</topic><topic>Picture languages</topic><topic>Pictures</topic><topic>Recognizability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Grandjean, Etienne</creatorcontrib><creatorcontrib>Olive, Frédéric</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Journal of computer and system sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Grandjean, Etienne</au><au>Olive, Frédéric</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A logical approach to locality in pictures languages</atitle><jtitle>Journal of computer and system sciences</jtitle><date>2016-09</date><risdate>2016</risdate><volume>82</volume><issue>6</issue><spage>959</spage><epage>1006</epage><pages>959-1006</pages><issn>0022-0000</issn><eissn>1090-2724</eissn><abstract>This paper deals with descriptive complexity of picture languages of any dimension by fragments of existential second-order logic:
1) We generalize to any dimension the characterization by Giammarresi et al. (1996) of the class of recognizable picture languages in existential monadic second-order logic.
2) We state natural logical characterizations of the class of picture languages of any dimension d≥1 recognized in linear time on nondeterministic cellular automata, a robust complexity class that contains, for d=1, all the natural NP-complete problems.
Our characterizations are essentially deduced from normalization results for first-order and existential second-order logics over pictures.
•The class of recognizable picture languages is characterized by existential monadic second-order logic.•Logical characterizations of the class of picture languages recognized in linear time on nondeterministic cellular automata.•This shows the logics involved can be made “local” with respect to the underlying regular structures.•Hierarchy results among some logical frameworks are deduced from the above.</abstract><pub>Elsevier Inc</pub><doi>10.1016/j.jcss.2016.01.005</doi><tpages>48</tpages><orcidid>https://orcid.org/0000-0002-3552-5566</orcidid><oa>free_for_read</oa></addata></record> |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Cellular automata Complexity Computational Complexity Computer Science Existential second-order logic Fragments Languages Linear time Locality and tiling Logic Logical characterizations Monadic second-order logic Picture languages Pictures Recognizability |
| title | A logical approach to locality in pictures languages |
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