Covering and separation for logical fragments with modular predicates
For every class $\mathscr{C}$ of word languages, one may associate a decision problem called $\mathscr{C}$-separation. Given two regular languages, it asks whether there exists a third language in $\mathscr{C}$ containing the first language, while being disjoint from the second one. Usually, finding...
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| Vydané v: | Logical methods in computer science Ročník 15, Issue 2 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Logical Methods in Computer Science Association
08.05.2019
Logical Methods in Computer Science e.V |
| Predmet: | |
| ISSN: | 1860-5974, 1860-5974 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | For every class $\mathscr{C}$ of word languages, one may associate a decision problem called $\mathscr{C}$-separation. Given two regular languages, it asks whether there exists a third language in $\mathscr{C}$ containing the first language, while being disjoint from the second one. Usually, finding an algorithm deciding $\mathscr{C}$-separation yields a deep insight on $\mathscr{C}$. We consider classes defined by fragments of first-order logic. Given such a fragment, one may often build a larger class by adding more predicates to its signature. In the paper, we investigate the operation of enriching signatures with modular predicates. Our main theorem is a generic transfer result for this construction. Informally, we show that when a logical fragment is equipped with a signature containing the successor predicate, separation for the stronger logic enriched with modular predicates reduces to separation for the original logic. This result actually applies to a more general decision problem, called the covering problem. |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.23638/LMCS-15(2:11)2019 |