Precongruence formats for decorated trace semantics

Abstract

This paper explores the connection between semantic equivalences and preorders for concrete sequential processes, represented by means of labeled transition systems, and formats of transition system specifications using Plotkin's structural approach. For several preorders in the linear timebranching time spectrum a format is given, as general as possible, such that this preorder is a precongruence for all operators specifiable in that format. The formats are derived using the modal characterizations of the corresponding preorders.

Logical Characterization of Trace Metrics

“…Since the same reasoning can be applied symmetrically to each α ∈ Tr(C max (z t )) we gather that also Tr(C max (z t )) ⊆ Tr(C max (z s )) holds. The two inclusions give us Equation (5). Finally, we aim to prove Equation (6).…”

“…the strong trace metric and its weak version, as well as the equivalences constituting their kernels. The logic L (and consequently L w ) can be seen either as a simplified version of the modal logic L from [13], which has been successfully employed in [9] to characterize the bisimilarity metric [7,12,14], or more simply as a probabilistic version of the logic characterizing the trace semantics in the fully nondeterministic case [5]. More precisely, L consists of two classes of formulae.…”

Modular Semantics for Transition System Specifications with Negative Premises

“…A widely accepted definition is based on well-supported proofs for transition formulae p l −→ q where p (and q) are closed terms [12,5]. Well-supported-proofs for open formulae has remained an open problem since 1995 [11] (and the task was characterised as 'somewhat problematic' by Van Glabbeek [12]).…”

Compositionality of Hennessy-Milner Logic through Structural Operational Semantics

“…In Bloom, Fokkink & van Glabbeek [4] a method is given for decomposing formulae from a fragment of HML with infinite conjunctions, with respect to terms from any process algebra that has a structural operational semantics in ntyft/ntyxt format [9] without lookahead. This format is a generalisation of the De Simone format, and still guarantees that bisimulation equivalence is a congruence.…”

“…In this paper the decomposition method from [4] is extended to full HML with infinite conjunction, again with respect to terms from any process algebra that has a structural operational semantics in ntyft/ntyxt format without lookahead.…”