Non-termination in idempotent semirings

Authors:
Peter Höfner;Georg Struth
Affiliations:
Department of Computer Science, University of Sheffield, United Kingdom;Department of Computer Science, University of Sheffield, United Kingdom
Venue:
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Year:
2008

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Abstract

We study and compare two notions of non-termination on idempotent semirings: infinite iteration and divergence. We determine them in various models and develop conditions for their coincidence. It turns out that divergence yields a simple and natural way of modelling infinite behaviour, whereas infinite iteration shows some anomalies.