Modularity of Convergence and Strong Convergence in Infinitary Rewriting
Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term Rewriting Systems that all reduction sequences converge to a...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2010-09-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/878/pdf |
| _version_ | 1797268806912966656 |
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| author | Stefan Michael Kahrs |
| author_facet | Stefan Michael Kahrs |
| author_sort | Stefan Michael Kahrs |
| collection | DOAJ |
| description | Properties of Term Rewriting Systems are called modular iff they are
preserved under (and reflected by) disjoint union, i.e. when combining two Term
Rewriting Systems with disjoint signatures. Convergence is the property of
Infinitary Term Rewriting Systems that all reduction sequences converge to a
limit. Strong Convergence requires in addition that redex positions in a
reduction sequence move arbitrarily deep. In this paper it is shown that both
Convergence and Strong Convergence are modular properties of non-collapsing
Infinitary Term Rewriting Systems, provided (for convergence) that the term
metrics are granular. This generalises known modularity results beyond metric
\infty. |
| first_indexed | 2024-04-25T01:38:20Z |
| format | Article |
| id | doaj.art-f24c4ce866794673bedc21b7a0e8e17d |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:38:20Z |
| publishDate | 2010-09-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-f24c4ce866794673bedc21b7a0e8e17d2024-03-08T09:12:33ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742010-09-01Volume 6, Issue 310.2168/LMCS-6(3:18)2010878Modularity of Convergence and Strong Convergence in Infinitary RewritingStefan Michael KahrsProperties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term Rewriting Systems that all reduction sequences converge to a limit. Strong Convergence requires in addition that redex positions in a reduction sequence move arbitrarily deep. In this paper it is shown that both Convergence and Strong Convergence are modular properties of non-collapsing Infinitary Term Rewriting Systems, provided (for convergence) that the term metrics are granular. This generalises known modularity results beyond metric \infty.https://lmcs.episciences.org/878/pdfcomputer science - logic in computer sciencecomputer science - formal languages and automata theoryf.4.2 |
| spellingShingle | Stefan Michael Kahrs Modularity of Convergence and Strong Convergence in Infinitary Rewriting Logical Methods in Computer Science computer science - logic in computer science computer science - formal languages and automata theory f.4.2 |
| title | Modularity of Convergence and Strong Convergence in Infinitary Rewriting |
| title_full | Modularity of Convergence and Strong Convergence in Infinitary Rewriting |
| title_fullStr | Modularity of Convergence and Strong Convergence in Infinitary Rewriting |
| title_full_unstemmed | Modularity of Convergence and Strong Convergence in Infinitary Rewriting |
| title_short | Modularity of Convergence and Strong Convergence in Infinitary Rewriting |
| title_sort | modularity of convergence and strong convergence in infinitary rewriting |
| topic | computer science - logic in computer science computer science - formal languages and automata theory f.4.2 |
| url | https://lmcs.episciences.org/878/pdf |
| work_keys_str_mv | AT stefanmichaelkahrs modularityofconvergenceandstrongconvergenceininfinitaryrewriting |