Causal ambiguity and partial orders in event structures

Event structure models often have some constraint which ensures that for each\ud system run it is clear what are the causal predecessors of an event (i.e. there is no causal ambiguity). In this contribution we study what happens if we remove\ud such constraints. We define five different partial order semantics that are intentional in the sense that they refer to syntactic aspects of the model. We also define an observational partial order semantics, that derives a partial order from just the event traces. It appears that this corresponds to the so-called early intentional semantics; the other intentional semantics cannot be observationally characterized. We study the equivalences induced by the different partial order definitions, and their interrelations

Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions

Stochastic simulation of event structures

Currently the semantics of stochastic process algebras are defined using (an extension) of labelled transition systems. This usually results in a semantics based on the interleaving of causally independent actions. The advantage is that the structure of transition systems closely resembles that of Markov chains, enabling the use of standard solution techniques for analytical and numerical performance assessment of formal specifications. The main drawback is that distributions are restricted to be exponential. In [2] we proposed to use a partial-order semantics for stochastic process algebras. This allows the support of non-exponential distributions in the process algebra in a perspicuous way, but the direct resemblance with Markov chains is lost. This paper proposes to exploit discrete-event simulation techniques for analyzing our partial-order model, called stochastic event structures. The key idea is to obtain from event structures so-called (time-homogeneous) generalized semiMarkov ..

Non-determinism in Probabilistic Timed Systems with General Distributions

n/

Reconciling real and stochastic time: The need for probabilistic refinement

We conservatively extend anACP-style discrete-time process theorywith discrete stochastic delays. The semantics of the timed delays relies on time additivity and time determinism, which are properties that enable us to merge subsequent timed delays and to impose their synchronous expiration. Stochastic delays, however, interact with respect to a so-called race condition that determines the set of delays that expire first, which is guided by an (implicit) probabilistic choice. The race condition precludes the property of time additivity as the merger of stochastic delays alters this probabilistic behavior. To this end, we resolve the race condition using conditionally- distributed unit delays. We give a sound and ground-complete axiomatization of the process theory comprising the standard set of ACP-style operators. In this generalized setting, the alternative composition is no longer associative, so we have to resort to special normal forms that explicitly resolve the underlying race condition. Our treatment succeeds in the initial challenge to conservatively extend standard time with stochastic time. However, the 'dissection' of the stochastic delays to conditionally-distributed unit delays comes at a price, as we can no longer relate the resolved race condition to the original stochastic delays. We seek a solution in the field of probabilistic refinements that enable the interchange of probabilistic and non deterministic choices.Fil: Markovski, J.. Technische Universiteit Eindhoven; Países BajosFil: D'argenio, Pedro Ruben. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Baeten, J. C. M.. Technische Universiteit Eindhoven; Países Bajos. Centrum Wiskunde & Informatica; Países BajosFil: De Vink, E. P.. Technische Universiteit Eindhoven; Países Bajos. Centrum Wiskunde & Informatica; Países Bajo