Simplified Coalgebraic Trace Equivalence

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Conference Proceeding

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The analysis of concurrent and reactive systems is based to a large degree on various notions of process equivalence, ranging, on the so-called lineartime/ 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. LTS. 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 LTS and probabilistic labelled transition systems.


This is a pre-copy-editing, author-produced PDF of a paper presented at Software, Services, and Systems in 2015 following peer review. The definitive publisher-authenticated version is available online at DOI: 10.1007/978-3-319-15545-6_8.