Submitted to: QFM 2009 c  F. Buti et al. This work is licensed under the Creative Commons Attribution License. Evaluating the Efficiency of Asynchronous Systems with ∗ F. Buti, M. Callisto, F. Corradini, M.R. Di Berardini Dipartimento di Matematica e Informatica, Università di Camerino W. Vogler Institut für Informatik, Universität Augsburg In this extended abstract we present a tool for evaluating the worst-case efficiency of asynchronous systems called (Fast Asynchronous Systems Evaluation). is based on PAFAS algebra theory and we used it to relate three different implementations of the same bounded buffer already studied in preview works. 1 Introduction PAFAS is a process algebra where basic actions are atomic and instantaneous but have associated a time bound interpreted as the maximal time delay for their execution. These upper time bounds can be used to evaluate efficiency, but they do not influence functionality (which actions are performed); so compared with CCS also PAFAS treats the full functionality of asynchronous systems. In [1], processes are compared via a variant of the testing approach developed by De Nicola and Hennessy [2]. Tests considered in [1] are test environments (as in [2]) together with a time bound. A process is embedded into the environment (via parallel composition) and satisfies a (timed) test if success is reached before the time bound in every run of the composed system, i.e. even in the worst case. This gives rise to a faster-than preorder relation over processes that is naturally an efficiency preorder. Furthermore, this efficiency preorder can be characterised as inclusion of a special kind of refusal traces which provide decidability of the testing preorder for finite state processes. In [3] it has been shown that the faster- than preorder of Corradini et al. [1] can equivalently be defined on the basis of a performance function that gives the worst-case time needed to satisfy any test environment (or user behaviour). Another main result in [3] shows that, whenever we adapt the timed testing scenario described above by considering only test environments that want n task to be performed as fast as possible, this performance function is asymptotically linear. This result provides us with a quantitative measure of systems performance, essentially a function (from natural numbers to natural numbers) - called response performance function - that evaluates how fast the system under consideration responds to requests from the environment. In this work we present , a corresponding tool implementing the PAFAS theory, developed at the University of Camerino that supports us to automatically evaluate the worst-case performance of a PAFAS process. With , we evaluated the efficiency of three different implementations of the same bounded buffer called (first-in-first-out queue), (sequence of cells connected end-to-end) and (an array ∗ This work was supported by the PRIN Project ‘Paco:Performability-Aware Computing: Logics, Models, and Languages’.