Sequential Composition in the Presence of Intermediate Termination (Extended Abstract)

Abstract

The standard operational semantics of the sequential composition operator gives rise to unbounded branching and forgetfulness when transparent process expressions are put in sequence. Due to transparency, the correspondence between context-free and pushdown processes fails modulo bisimilarity, and it is not clear how to specify an always terminating half counter. We propose a revised operational semantics for the sequential composition operator in the context of intermediate termination.With the revised operational semantics, we eliminate transparency, allowing us to establish a close correspondence between context-free processes and pushdown processes. Moreover, we prove the reactive Turing powerfulness of TCP with iteration and nesting with the revised operational semantics for sequential composition.

Divergence-Preserving Branching Bisimilarity

“…A calculus with constants for deadlock and successful termination, unary action prefixes, binary operations for non-deterministic choice, sequencing and ACP-style parallel composition, iteration and nesting is both executable and behaviourally complete up to divergence-preserving branching bisimilarity [3]. The π-calculus is also behaviourally complete up to divergence-preserving branching bisimilarity.…”

“…These formats relax the requirements of the branching bisimulation and rooted branching bisimulation formats of [10]. The relaxation of the formats is meaningful: the processalgebraic operations for priority [1] and sequencing [5,4,3], with which (rooted) branching bisimilarity is not compatible, are in the rooted divergence-preserving branching bisimulation format. So, in contrast to its divergence-insensitive variant, rooted divergence-preserving branching bisimilarity is compatible with priority and sequencing.…”

Divide and congruence III: From decomposition of modal formulas to preservation of stability and divergence

“…In [2], it was argued that an adaptation of the classical operational semantics of sequential composition in a process theory with the empty process leads to a smoother integration of classical automata theory. A detailed proof is given that rooted divergence-preserving branching bisimilarity is a congruence for the resulting operator-here called sequencing-, but also it is observed that this property can be inferred from our congruence format.…”