Relating processes with respect to speed

In this paper, we consider the problem of defining a preorder on concurrent processes which will distinguish between functionally behaviourally equivalent processes which operate at different speeds. As our basic framework, we use a subset of the calculus TCCS of [Mol90], a language for describing concurrent processes involving timing constraints.There is an anomaly in timed process calculi such as TCCS which nullifies the possibility of defining such a preorder which is a precongruence. This anomaly arises due to the nature of the constructs in the calculus which force events to be executed without delay. To rectify this conflict, we define and motivate the above mentioned subcalculus, which we call ℓTCCS (loose TCCS), and define our relation over this language. ℓTCCS is precisely TCCS where all events may delay indefinitely before executing. We demonstrate why this is necessary in order for any sensible faster than relation to be a precongruence.Upon providing the semantic definition of our “faster than” relation, we give results on the precongruicity of the relation and present a set of inequational laws.