Unifying the Linear Time-Branching Time Spectrum of Process Semantics

Abstract

Abstract. Van Glabbeek's linear time-branching time spectrum is one of the most relevant work on comparative study on process semantics, in which semantics are partially ordered by their discrimination power. In this paper we bring forward a refinement of this classification and show how the process semantics can be dealt with in a uniform way: based on the very natural concept of constrained simulation we show how we can classify the spectrum in layers; for the families lying in the same layer we show how to obtain in a generic way equational, observational, logical and operational characterizations; relations among layers are also very natural and differences just stem from the constraint imposed on the simulations that rule the layers. Our methodology also shows how to achieve a uniform treatment of semantic preorders and equivalences. ACM CCS: [Theory of computation]:Formal languages and automata theory-FormalismsAlgebraic language theory; Formal languages and automata theory-Semantics and reasoning-Program semantics; Logic; Models of computation-Concurrency.

On the Axiomatisability of Parallel Composition

“…In [dFGPR13] an alternative classification of the equivalences in the spectrum with respect to [Gla01] was proposed. In order to obtain a general, unified, view of process semantics, the spectrum was divided into layers, each corresponding to a different notion of constrained simulation [dFG08].…”

“…In order to obtain a general, unified, view of process semantics, the spectrum was divided into layers, each corresponding to a different notion of constrained simulation [dFG08]. There are pleasing connections between the different layers and the partitioning they induce of the congruences in the spectrum, as given in [dFGPR13], and the relationships between the axioms for the interleaving operator we have presented in this study.…”

When Are Prime Formulae Characteristic?

“…We reason about characterization by primality (Theorem 5) by showing that each logic is finitely characterized by some monotonic B, and by building, for each characteristic formula χ(p), a formula χ(p) with the properties specified in Proposition 5(iii). The logics we focus on are the ones for the semantics in van Glabbeek's branching-time spectrum [8,9], namely simulation (S), complete simulation (CS), ready simulation (RS), trace simulation (TS), 2-nested simulation (2S), and bisimulation (BS). Their syntax and semantics are briefly described in what follows.…”

“…Theorem 4 (Logical characterization [8,9]). For each X ∈ spectrum and for all p, q ∈ P , p X q iff L X (p) ⊆ L X (q).…”

“…In this approach, checking whether a system correctly implements its specification amounts to verifying whether the state machines describing them are related by some suitable notion of behavioural equivalence/preorder. (See [8,9] for taxonomic studies of the plethora of behavioural relations that have been considered in the field of concurrency theory. )…”