Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract)
The languages accepted by finite automata are precisely the languages denoted by regular expressions. In contrast, finite automata may exhibit behaviours that cannot be described by regular expressions up to bisimilarity. In this paper, we consider extensions of the theory of regular expressions wit...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Open Publishing Association
2010-11-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1011.6429v1 |
| _version_ | 1818937010282299392 |
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| author | Jos C. M. Baeten Bas Luttik Tim Muller Paul van Tilburg |
| author_facet | Jos C. M. Baeten Bas Luttik Tim Muller Paul van Tilburg |
| author_sort | Jos C. M. Baeten |
| collection | DOAJ |
| description | The languages accepted by finite automata are precisely the languages denoted by regular expressions. In contrast, finite automata may exhibit behaviours that cannot be described by regular expressions up to bisimilarity. In this paper, we consider extensions of the theory of regular expressions with various forms of parallel composition and study the effect on expressiveness. First we prove that adding pure interleaving to the theory of regular expressions strictly increases its expressiveness up to bisimilarity. Then, we prove that replacing the operation for pure interleaving by ACP-style parallel composition gives a further increase in expressiveness. Finally, we prove that the theory of regular expressions with ACP-style parallel composition and encapsulation is expressive enough to express all finite automata up to bisimilarity. Our results extend the expressiveness results obtained by Bergstra, Bethke and Ponse for process algebras with (the binary variant of) Kleene's star operation. |
| first_indexed | 2024-12-20T05:45:09Z |
| format | Article |
| id | doaj.art-0b8a6a1712414e8483575c0c88515452 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-12-20T05:45:09Z |
| publishDate | 2010-11-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-0b8a6a1712414e8483575c0c885154522022-12-21T19:51:20ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802010-11-0141Proc. EXPRESS 201011510.4204/EPTCS.41.1Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract)Jos C. M. BaetenBas LuttikTim MullerPaul van TilburgThe languages accepted by finite automata are precisely the languages denoted by regular expressions. In contrast, finite automata may exhibit behaviours that cannot be described by regular expressions up to bisimilarity. In this paper, we consider extensions of the theory of regular expressions with various forms of parallel composition and study the effect on expressiveness. First we prove that adding pure interleaving to the theory of regular expressions strictly increases its expressiveness up to bisimilarity. Then, we prove that replacing the operation for pure interleaving by ACP-style parallel composition gives a further increase in expressiveness. Finally, we prove that the theory of regular expressions with ACP-style parallel composition and encapsulation is expressive enough to express all finite automata up to bisimilarity. Our results extend the expressiveness results obtained by Bergstra, Bethke and Ponse for process algebras with (the binary variant of) Kleene's star operation.http://arxiv.org/pdf/1011.6429v1 |
| spellingShingle | Jos C. M. Baeten Bas Luttik Tim Muller Paul van Tilburg Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract) Electronic Proceedings in Theoretical Computer Science |
| title | Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract) |
| title_full | Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract) |
| title_fullStr | Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract) |
| title_full_unstemmed | Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract) |
| title_short | Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract) |
| title_sort | expressiveness modulo bisimilarity of regular expressions with parallel composition extended abstract |
| url | http://arxiv.org/pdf/1011.6429v1 |
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