TY  - JOUR
A1  - Desharnais, Jules
A1  - Möller, Bernhard
A1  - Struth, Georg
T1  - Algebraic Notions of Termination
T2  - Logical Methods in Computer Science
N2  - 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.
Y1  - 2018
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/38930
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-389300
VL  - 7
IS  - 1
SP  - 1
EP  - 29
ER  -