# Completeness in real time process algebra

## Abstract

Recently, J.C.M. Baeten and J.A. Bergstra extended ACP with real time, resulting in a Real Time Process Algebra, called ACP_{ρ} [BB91]. They introduced an equational theory and an operational semantics. However, their work does not contain a completeness result nor does it contain the definitions to give proofs in detail. In this paper we introduce some machinery and a completeness result.

The operational semantics of [BB91] contains the notion of an *idle* step reflecting that a process can do nothing more then passing the time before performing a concrete action at a certain point in time. This *idle* step corresponds nicely to our intuition but it results in infinitary transition systems. In this paper we give a more abstract operational semantics, by abstracting from the *idle* step. Due to this simplification we can prove soundness and completeness easily. These results hold for the semantics of [BB91] as well, since both operational semantics induce the same equivalence relation between processes.

## 1985 Mathematics Subject Classification

68Q10 68Q40 68Q45 68Q55## 1982 CR Categories

D.1.3 D.3.1 D.4.1 F.1.2 F.3.2## Key Words & Phrases

Real Time Process Algebra ACP Integration SOS## Preview

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