Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version of the Timed Probabilistic concurrent Computation Tree Logic (TPCTL) of Hansson. The definitions are made, and the evaluations carried out, in terms of a general labeled transition system model for concurrent probabilistic computation. The results cover weak simulations, which abstract from internal computation, as well as strong simulations, which do not.

ion Let E; E 0 be PCCS expressions. The inter-model abstraction rule IMARGR is defined by E ff[p] \Gamma\Gamma! i E 0 =) E ff[p= G (E;fffg)] ae \Gamma\Gamma\Gamma\Gamma\Gamma\Gamma! i E 0 This rule uses the generative normalization function to convert generative probabilities to reactive ones, thereby abstracting away from the relative probabilities between different actions. We can now define 'GR ('G (P )) as the reactive transition system that can be inferred from P 's generative transition system via IMARGR . By the same procedure as described at the end of Section 3.1, 'GR can be extended to a mapping 'GR : j GG ! j GR . Write P GR ¸ Q if P; Q 2 Pr are reactive bisimulation equivalent with respect to the transitions derivable from G+IMARGR , i.e. the theory obtained by adding IMARGR to the rules of Figure 7. The equivalence GR ¸ is defined just like R ¸ but using the cPDF ¯GR instead of ¯R . ¯GR is defined by ¯GR (P; ff; S) = X i2I R (=I G ) fj p i j G+ I...

. In this paper we investigate ways of modelling communicating processes that display both nondeterministic and probabilistic behaviour. We present an operational model for a probabilistic version of CSP, and describe a number of ways of abstracting a denotational semantics from such a model, so as to represent a process by a set of probability functions, one function for each way of resolving the nondeterministic choices. We then prove an interesting--- although disappointing---result, which shows that no such denotational model can be compositional. We end by identifying a problem with the operational model, which is shared by all similar models known to us, and briefly give some indications as to how this problem might be overcome. 1. Introduction In recent years, an important problem in the study of communicating systems has been the modelling of probabilistic behaviour. This is necessary if we are to argue formally about unreliable behaviour (for example that displayed by an unre...

. Transition systems are a basic semantic model for formal description, specification, and analysis of concurrent and distributed systems. In order to describe and analyze aspects of reliability, such as the likelihood of trace and failure, this model has been extended in various ways to handle probabilistic behavior. To use these models for specification and stepwise development of systems, it is important to develop appropriate refinement preorders. In the paper, we develop refinement preorders based on a framework of testing for a model that represents both nondeterministic and probabilistic choices as independent concepts [YL92]. Our main contribution is a notion of reward testing, and a denotational characterization of a testing preorder, which corresponds to a natural probabilistic extension of the trace model [Hoa85]. 1 Introduction Transition systems are well-established as a basic semantic model for the formal description, specification, and analysis of concurrent and distrib...

In this paper we describe a way of modelling communicating processes that display both nondeterministic and probabilistic behaviour. We represent processes by nondeterministic, probabilistic, action (NPA) graphs with three sorts of nodes: action nodes, from which the process may evolve by performing visible actions; probabilistic nodes, from which the process may evolve probabilistically; and nondeterministic nodes, from which the process may evolve nondeterministically. We define a number of types of "observation"---such as traces and refusals--- that can be made of processes. For each type of observation, we describe how to abstract a corresponding denotational semantics from an NPA graph, so as to represent a process by a set of probability functions on observations---one function for each way of resolving the nondeterministic choices. We illustrate our approach by using it to give a semantic model to a probabilistic version of CSP: we give an operational semantics for the language ...

In this paper we present a probabilistic extension of LOTOS which is upward compatible with LOTOS. We present testing semantics for the reactive and generative models described in [vGSST90]. While there is a certain lose of the meaning of probabilities in the reactive model, testing with probabilistic tests proves to be too strong, because it does not relate behavior expressions which we expect to be equivalent. This is why we introduce the limited generative model, where tests are not allowed to have explicit probabilities. We give a fully abstract characterization for the reactive model, while we give alternative characterizations (based on a set of essential tests) for the generative and limited generative models. We also present some algebraic laws for each of the models, including some laws which establish the difference between the three models.

In this paper we introduce a new Stochastic Process Algebra: NMSPA. This new language presents the usual features of stochastic models but probability distributions are not restricted to be exponential. This fact increases the expressive power of the language in several ways. For example, we can specify actions that can be executed with probability 1 in a finite amount of time, so-called passive actions fall in a natural way inside our framework, urgency of internal actions can be expressed, etc. In order to define an interleaving semantics for the parallel operator, we benefit from ideas used in timed process algebras. Our operational transitions include information about the time when actions can be executed, as well as the random variable associated with them. We provide our language with a notion of strong bisimulation which takes into account urgency of internal transitions. Finally, we specify the Alternating Bit Protocol. This is a very simple communication protocol where th...

. We propose a fully parallel calculus of synchronizing processes. The calculus was deeply inspired by LOTOS, of which it inherits multi-party synchronization in process parallel composition. On the other hand, its semantics is not interleaving whereas LOTOS one is. The model we propose is somehow in between Milner's SCCS and ASCCS in that independent actions are performed simultaneously, whereas synchronization is achieved by means of delay. Also, delay is controlled in the sense that no process can delay an action if the environment allows that action to be performed. The calculus we propose here was originally designed as a first step towards a probabilistic one. Nevertheless we think that the pure version of the calculus has some features which are interesting on their own. As an example we use it to describe a quite simple system which may be thought of as a possible fault tolerant architecture for a hardware component. We also provide a set of equational laws based o...

In this paper, we study behaviour descriptions with uncertain information such as "the probability of a system failure within a given time period is less than or equal to 0:3" in terms of process algebras. Typical systems that may show such behaviours include communicating systems with unreliable components, e.g. faulty medium. We present a process model for such behaviours, in which uncertain information is described by means of intervals of probabilities. In particular, we introduce a stochastic choice operator P ffi [OE i ]E i , where OE i 's are intervals of probabilities. Roughly speaking, it is a process which may become E i in one unit of time with a probability within the interval OE i . Such a process is considered as a specification specifying a set of processes with less uncertain information. We develop a notion of probabilistic simulation to order specifications in terms of the degree of uncertainty in the specifications, which generalize the notion of probabilistic bisi...

This document describes the research projects of the Formal Methods and Tools research groups of the department of Tele-Informatics and Open Systems at the Faculty of Computers Science of the University of Twente. 1 Valide 1. Project name: Valide (version 1) 2. Project period: starting date: 1 January 1994 duration: indefinite 3. Project leaders: prof. dr Ed Brinksma dr Henk Alblas 4. Coordinating department: INF/TIOS 5. Embedding: Valide is part of the VF--research programme on Tele-Informatics and Open Systems. As such it is part of the TIOS participation in the research programme of the Centre for Tele-Informatics and Information Technology (CTIT). The subprojects participate in a number of international research programmes such as ESPRIT Basic Research Action and RACE, as well as national projects funded by NWO. The Valide subprojects are: ffl Leibniz (Transformational Design of Distributed Systems) ffl Popper (Validation of Distributed System Design) ffl Plato (Specificati...