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.
They generate this inequational axiomatization by simply adding the defining inequational axioms for the ready simulation preorder to the axiomatization for the equivalence-see Theorem 5.1 in REF .
Simulations up-to and Canonical Preorders (extended abstract) Abstract
Electron. Notes Theor. Comput. Sci.
Electron. Notes Theor. Comput. Sci.
Computer Science