Jules, Desharnais and Moeller, Bernhard and Georg, Struth - Algebraic Notions of Termination

lmcs:777 - Logical Methods in Computer Science, February 11, 2011, Volume 7, Issue 1
Algebraic Notions of Termination

Authors: Jules, Desharnais and Moeller, Bernhard and Georg, Struth

Five algebraic notions of termination are formalised, analysed and compared: wellfoundedness or Noetherity, L\"ob'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.

Source : oai:arXiv.org:1012.5803
DOI : 10.2168/LMCS-7(1:1)2011
Volume: Volume 7, Issue 1
Published on: February 11, 2011
Submitted on: July 28, 2006
Keywords: Computer Science - Logic in Computer Science,F.3.1, F.3.2, F.4.1


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