Algebraic notions of nontermination: Omega and divergence in idempotent semirings
Two notions of nontermination are studied and compared in the setting of idempotent semirings: Cohen's omega operator and a divergence operator. They are determined for various computational models, and conditions for their existence and their coincidence are given. It turns out that divergence yields a simple and natural way of modelling infinite behaviours of programs and discrete systems, whereas the omega operator shows some anomalies. (C) 2010 Elsevier Inc. All rights reserved.
nontermination omega divergence idempotent semirings modal semirings recursion and corecursion