Contextual equivalences in configuration structures and reversibility

Abstract

Contextual equivalence equate terms that have the same observable behaviour in any context. A standard contextual equivalence for CCS is the strong barbed congruence. Configuration structures are a denotational semantics for processes in which one define equivalences that are more discriminating, i.e. that distinguish the denotation of terms equated by barbed congruence. Hereditary history preserving bisimulation (HHPB) is such a relation. We define a strong backand-forth barbed congruence on RCCS, a reversible variant of CCS. We show that the relation induced by the back-and-forth congruence on configuration structures is equivalent to HHPB, thus providing a contextual characterization of HHPB.

Event structure semantics of (controlled) reversible CCS

“…We have defined a category of reversible bundle event structures, and used the causal subcategory to model uncontrolled CCSK. Unlike previous work giving a truly concurrent semantics of a reversible process calculus using rigid families [6] or configuration structures [1], we have used the way CCSK handles past actions to generate both the event structure and the initial state directly from the process, rather than needing to first undo past actions to get the original process and from there the rigid family or configuration structure, and then redo the actions to get the initial state.…”

“…However, their semantics requires a process to first reverse all actions to find the original process, map this process to a rigid family, and then apply each of the reversed memories in order to reach the current state of the process. Aubert and Cristescu [1] used a similar approach to describe the semantics of RCCS processes without auto-concurrency, auto-conflict, or recursion as configuration structures. By contrast, we map a CCSK process (with auto-concurrency, auto-conflict, and recursion) with past actions directly to a (reversible) event structure in a strictly denotational fashion.…”

Causally consistent reversible choreographies

“…We shall work with binary relations on configurations, wri en ℜ ⊆ M × M. We now adapt the classical notion of barbs [21] to our se ing: rather than communication subjects (which are hidden/unobservable names in intra-session communications), it suffices to use participant identities as observables: Notice that our definition of barbs is connected to the notion of stability: since in M ⇂ p we require a monitor with empty tag, this ensures that p is not involved in an ongoing backward step. In a way, this allows us to consider just forward barbs (as in [1]). We now adapt the definition of weak barbed back-and-forth (bf) bisimulation and congruence [15] in order to work with decoupled and atomic reduction semantics: We now may state our second connection between decoupled and atomic reductions: By observing that the set of atomic configurations is a subset of reachable configurations, this result can also be formulated as full abstraction.…”

Forward-Reverse Observational Equivalences in CCSK

“…Given the relevance of analysis techniques for concurrent systems, also a number of analysis techniques have been considered, e.g., following the session types approach [27,3,7]. Notions of observational equivalence have also been used in a few works, such as [30,26,1,2], yet the question of which notions of observational equivalence are suitable for reversible processes, and how they can be exploited to actually reason about them, has seldom been considered.…”