Another look at abstraction in process algebra: Extended abstract

Central to theories of concurrency is the notion of abstraction. Abstraction from internal actions is the most important tool for system verification. In this paper, we look at abstraction in the framework of the Algebra of Communicating Processes (see BERGSTRA & KLOP [4, 6]). We introduce a hidden step η, and construct a model for the resulting theory ACPη. We briefly look at recursive specifications in this theory, and discuss the relations with Milner's silent step τ

Another look at abstraction in process algebra: Extended abstract

Central to theories of concurrency is the notion of abstraction. Abstraction from internal actions is the most important tool for system verification. In this paper, we look at abstraction in the framework of the Algebra of Communicating Processes (see BERGSTRA & KLOP [4, 6]). We introduce a hidden step η, and construct a model for the resulting theory ACPη. We briefly look at recursive specifications in this theory, and discuss the relations with Milner's silent step τ

Delayed choice for process algebra with abstraction

The delayed choice is an operator which serves to combine linear time and branching time within one process algebra. We study this operator in a theory with abstraction, more precisely, in a setting considering branching bisimulation. We show its use in scenario specifications and in verification to reduce irrelevant branching structure of a process

Branching time and orthogonal bisimulation equivalence

We propose a refinement of branching bisimulation equivalence that we call orthogonal bisimulation equivalence. Typically, internal activity (i.e., the performance of $tau$-steps) may be compressed, but not completely discarded. Hence, a process with $tau$-steps cannot be equivalent to one without $tau$-steps. Also, we present a modal characterization of orthogonal bisimulation equivalence. This equivalence is a congruence for ACP extended with abstraction and priority operations. We provide a complete axiomatization, and describe some expressiveness results. Finally, we present the verification of a PAR protocol that is specified with use of priorities

A Calculus for Timed Automata (Extended Abstract)

A language for representing timed automata is introduced. Its semantics i defined in terms of timed automata. This language is complete in the sense that any timed automaton can be represented by a term in the language. We also define a direct operational semantics for the language in terms of (timed) transition systems. This is proven to be equivalent (or, more precisely, timed bisimilar) to the interpretation in terms of timed automata. In addition, a set of axioms is given that is shown to be sound for timed bisimulation. Finally, we introduce several features including the parallel composition and derived time operations like wait, time-out and urgency. We conclude with an example and show that we can eliminate non-reachable states using algebraic techniques

Parallel Pushdown Automata and Commutative Context-Free Grammars in Bisimulation Semantics (Extended Abstract)

A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In previous work, we proved the pendant of this theorem in a setting with interaction: the set of processes given by a pushdown automaton coincides with the set of processes given by a finite guarded recursive specification over a process algebra with actions, choice, sequencing and guarded recursion, if and only if we add sequential value passing. In this paper, we look what happens if we consider parallel pushdown automata instead of pushdown automata, and a process algebra with parallelism instead of sequencing.Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.05788. arXiv admin note: text overlap with arXiv:2203.0171