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Simulations up-to and canonical preorders



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Frutos Escrig, David de and Gregorio Rodríguez, Carlos (2007) Simulations up-to and canonical preorders. Electronic Notes in Theoretical Computer Science, 192 (1). pp. 13-28. ISSN 15710661

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Official URL: http://www.sciencedirect.com/science/article/pii/S1571066107005749


In this paper we define simulations up-to a preorder and show how we can use them to provide a coinductive, simulation-like, characterization of semantic preorders for processes. The result applies to a wide class of preorders, in particular to all semantic preorders coarser than the ready simulation preorder in the linear time-branching time spectrum. An interesting but unexpected result is that, when built from an equivalence relation, the simulation up-to is a canonical preorder whose kernel is the given equivalence relation. These canonical preorders have several nice properties, the main being that since all of them are defined in a homogeneous way, their properties can be proved in a generic way. In particular, we present an axiomatic characterization of each of these canonical preorders, that is obtained just by adding a single axiom to the axiomatization of the original equivalence relation. This gives us an alternative axiomatization for every axiomatizable preorder in the linear time-branching time spectrum, whose correctness and completeness can be proved once and for all.

Item Type:Article
Additional Information:

Proceedings of the Fourth Workshop on Structural Operational Semantics (SOS 2007)

Uncontrolled Keywords:processes; semantic preorders; simulations up-to; linear time-branching time spectrum
Subjects:Sciences > Computer science
ID Code:20675
Deposited On:05 Apr 2013 11:46
Last Modified:10 Aug 2018 08:16

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