Software, Services, and Systems pp 75-90

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8950) | Cite as

Simplified Coalgebraic Trace Equivalence

  • Alexander Kurz
  • Stefan Milius
  • Dirk Pattinson
  • Lutz Schröder

Abstract

The analysis of concurrent and reactive systems is based to a large degree on various notions of process equivalence, ranging, on the so-called linear-time/branching-time spectrum, from fine-grained equivalences such as strong bisimilarity to coarse-grained ones such as trace equivalence. The theory of concurrent systems at large has benefited from developments in coalgebra, which has enabled uniform definitions and results that provide a common umbrella for seemingly disparate system types including non-deterministic, weighted, probabilistic, and game-based systems. In particular, there has been some success in identifying a generic coalgebraic theory of bisimulation that matches known definitions in many concrete cases. The situation is currently somewhat less settled regarding trace equivalence. A number of coalgebraic approaches to trace equivalence have been proposed, none of which however cover all cases of interest; notably, all these approaches depend on explicit termination, which is not always imposed in standard systems, e.g. labelled transition systems. Here, we discuss a joint generalization of these approaches based on embedding functors modelling various aspects of the system, such as transition and braching, into a global monad; this approach appears to cover all cases considered previously and some additional ones, notably standard and probabilistic labelled transition systems.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Alexander Kurz
    • 1
  • Stefan Milius
    • 3
  • Dirk Pattinson
    • 2
  • Lutz Schröder
    • 3
  1. 1.University of LeicesterUK
  2. 2.The Australian National UniversityAustralia
  3. 3.Friedrich-Alexander-Universität Erlangen-NürnbergGermany

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