Algebraic Notions of Termination
- Five algebraic notions of termination are formalised, analysed and compared: wellfoundedness or Noetherity, Löb’s formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings, which are additively idempotent semirings with forward and backward modal operators. To model infinite behaviours, idempotent semirings are extended to divergence semirings, divergence Kleene algebras and omega algebras. The resulting notions and techniques are used in calculational proofs of classical theorems of rewriting theory. These applications show that modal semirings are powerful tools for reasoning algebraically about the finite and infinite dynamics of programs and transition systems.
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| Author: | Jules DesharnaisGND, Bernhard MöllerGND, Georg StruthGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-389300 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/38930 |
| Parent Title (English): | Logical Methods in Computer Science |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2011 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2018/07/23 |
| Volume: | 7 |
| Issue: | 1 |
| First Page: | 1 |
| Last Page: | 29 |
| DOI: | https://doi.org/10.2168/LMCS-7(1:1)2011 |
| Institutes: | Fakultät für Angewandte Informatik |
| Fakultät für Angewandte Informatik / Institut für Informatik | |
| Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
