Two-variable Logic with Counting and a Linear Order
We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of two linear orders (in the presence of two other binary symbol...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2016-06-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/1640/pdf |
| _version_ | 1797268657123885056 |
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| author | Witold Charatonik Piotr Witkowski |
| author_facet | Witold Charatonik Piotr Witkowski |
| author_sort | Witold Charatonik |
| collection | DOAJ |
| description | We study the finite satisfiability problem for the two-variable fragment of
first-order logic extended with counting quantifiers (C2) and interpreted over
linearly ordered structures. We show that the problem is undecidable in the
case of two linear orders (in the presence of two other binary symbols). In the
case of one linear order it is NEXPTIME-complete, even in the presence of the
successor relation. Surprisingly, the complexity of the problem explodes when
we add one binary symbol more: C2 with one linear order and in the presence of
other binary predicate symbols is equivalent, under elementary reductions, to
the emptiness problem for multicounter automata. |
| first_indexed | 2024-04-25T01:35:57Z |
| format | Article |
| id | doaj.art-bd834f6057fc473a8de9d11e7a85a262 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:35:57Z |
| publishDate | 2016-06-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-bd834f6057fc473a8de9d11e7a85a2622024-03-08T09:43:58ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742016-06-01Volume 12, Issue 210.2168/LMCS-12(2:8)20161640Two-variable Logic with Counting and a Linear OrderWitold CharatonikPiotr Witkowskihttps://orcid.org/0000-0002-1908-0827We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of two linear orders (in the presence of two other binary symbols). In the case of one linear order it is NEXPTIME-complete, even in the presence of the successor relation. Surprisingly, the complexity of the problem explodes when we add one binary symbol more: C2 with one linear order and in the presence of other binary predicate symbols is equivalent, under elementary reductions, to the emptiness problem for multicounter automata.https://lmcs.episciences.org/1640/pdfcomputer science - logic in computer science |
| spellingShingle | Witold Charatonik Piotr Witkowski Two-variable Logic with Counting and a Linear Order Logical Methods in Computer Science computer science - logic in computer science |
| title | Two-variable Logic with Counting and a Linear Order |
| title_full | Two-variable Logic with Counting and a Linear Order |
| title_fullStr | Two-variable Logic with Counting and a Linear Order |
| title_full_unstemmed | Two-variable Logic with Counting and a Linear Order |
| title_short | Two-variable Logic with Counting and a Linear Order |
| title_sort | two variable logic with counting and a linear order |
| topic | computer science - logic in computer science |
| url | https://lmcs.episciences.org/1640/pdf |
| work_keys_str_mv | AT witoldcharatonik twovariablelogicwithcountingandalinearorder AT piotrwitkowski twovariablelogicwithcountingandalinearorder |