A criterion for separating process calculi

We introduce a new criterion, replacement freeness, to discern the relative expressiveness of process calculi. Intuitively, a calculus is strongly replacement free if replacing, within an enclosing context, a process that cannot perform any visible action by an arbitrary process never inhibits the capability of the resulting process to perform a visible action. We prove that there exists no compositional and interaction sensitive encoding of a not strongly replacement free calculus into any strongly replacement free one. We then define a weaker version of replacement freeness, by only considering replacement of closed processes, and prove that, if we additionally require the encoding to preserve name independence, it is not even possible to encode a non replacement free calculus into a weakly replacement free one. As a consequence of our encodability results, we get that many calculi equipped with priority are not replacement free and hence are not encodable into mainstream calculi like CCS and pi-calculus, that instead are strongly replacement free. We also prove that variants of pi-calculus with match among names, pattern matching or polyadic synchronization are only weakly replacement free, hence they are separated both from process calculi with priority and from mainstream calculi.Comment: In Proceedings EXPRESS'10, arXiv:1011.601

A Calculus for Orchestration of Web Services

Service-oriented computing, an emerging paradigm for distributed computing based on the use of services, is calling for the development of tools and techniques to build safe and trustworthy systems, and to analyse their behaviour. Therefore, many researchers have proposed to use process calculi, a cornerstone of current foundational research on specification and analysis of concurrent, reactive, and distributed systems. In this paper, we follow this approach and introduce CWS, a process calculus expressly designed for specifying and combining service-oriented applications, while modelling their dynamic behaviour. We show that CWS can model all the phases of the life cycle of service-oriented applications, such as publication, discovery, negotiation, orchestration, deployment, reconfiguration and execution. We illustrate the specification style that CWS supports by means of a large case study from the automotive domain and a number of more specific examples drawn from it

A randomized encoding of the pi-calculus with mixed choice

International audienceWe consider the problem of encoding the pi-calculus with mixed choice into the asynchronous pi-calculus via a uniform translation while preserving a reasonable semantics. Although it has been shown that this is not possible with an exact encoding, we suggest a randomized approach using a probabilistic extension of the asynchronous pi-calculus, and we show that our solution is correct with probability 1 under any proper adversary wrt a notion of testing semantics. This result establishes the basis for a distributed and symmetric implementation of mixed choice which, differently from previous proposals in literature, does not rely on assumptions on the relative speed of processes and it is robust to attacks of proper adversaries

Revisiting Glue Expressiveness in Component-Based Systems

International audienceWe take a fresh look at the expressivity of BIP, a recent influential formal component model developed by J. Sifakis et al. We introduce a process calculus, called CAB, that models composite components as the combination of a glue (using BIP terminology) and subcomponents, and that constitutes a conservative extension of BIP with more dynamic forms of glues. We study the Turing completeness of CAB variants that differ only in their language for glues. We show that limiting the glue language to BIP glues suffices to obtain Turing-completeness, whereas removing priorities from the control language loses Turing-completeness. We also show that adding a simple form of dynamic component creation in the control language without priorities is enough to regain Turing completeness. These results complement those obtained on BIP, highlighting in particular the key role of priorities for expressivity

On the Expressivity of Infinite and Local Behaviour in Fragments of the pi-calculus

The pi-calculus [61] is one the most influential formalisms for modelling and analyzing the behaviour of concurrent systems. This calculus provides a language in which the structure of terms represents the structure of processes together with an operational semantics to represent computational steps. For example, the parallel composition term P | Q, which is built from the terms P and Q, represents the process that results from the parallel execution of the processes P and Q. Similarly, the restriction (v x)P represents a process P with local resource x. The replication !P can be thought of as abbreviating the parallel composition P | P | . . . of an unbounded number of P processes. As for other language-based formalisms (e.g., logic, formal grammars and the pi-calculus) a fundamental part of the research in process calculi involves the study of the expressiveness of fragments or variants of a given process calculus. In this dissertation we shall study the expressiveness of some variants of the pi-calculus focusing on the role of the terms used to represent local and infinite behaviour, namely restriction and replication. The first part of this dissertation is devoted to the expressiveness of the zero-adic variant of the (polyadic) pi-calculus, i.e., CCS with replication (CCS!) [21]. Busi et al [22] show that CCS! is Turing powerful [22]. The result is obtained by encoding Random Access Machines (RAMs) in CCS!. The encoding is said to be non-faithful because it may move from a state which can lead to termination into a divergent one which do not correspond to any configuration of the encoded RAM. I.e., the encoding is not termination preserving. In this dissertation we shall study the existence of faithful encodings into CCS! of models of computability strictly less expressive than Turing Machines. Namely, grammars of Types 1 (Context Sensitive Languages), 2 (Context Free Languages) and 3 (Regular Languages) in the Chomsky Hierarchy. We provide faithful encodings of Type 3 grammars. We show that it is impossible to provide a faithful encoding of Type 2 grammars and that termination-preserving CCS! processes can generate languages which are not Type 2. We finally conjecture that the languages generated by termination-preserving CCS! processes are Type 1 . We also observe that the encoding of RAMs [22] and several encoding of Turing-powerful formalisms in pi-calculus variants may generate an unbounded number of restrictions during the simulation of a given machine. This unboundedness arises from having restrictions under the scope of replication (or recursion) as in e.g., !(v x)P or μX.(v x)(P | X). This suggests that such an interplay between these operators is fundamental for Turing completeness. We shall also study the expressive power of restriction and its interplay with replication. We do this by considering several syntactic variants of CCS! which differ from each other in the use of restriction with respect to replication. We consider three syntactic variations of CCS! which do not allow the generation of unbounded number of restrictions: C2 is the fragment of CCS! not allowing restrictions under the scope of a replication, C3 is the restriction-free fragment of CCS!. The third variant is C4 which extends C2 with Phillips' priority guards [76]. We shall show that the use of an unboundedly many restrictions in CCS! is necessary for obtaining Turing expressiveness in the sense of Busi et al [22]. We do this by showing that there is no encoding of RAMs into C2 which preserves and reflects convergence. We also prove that up to failures equivalence, there is no encoding from CCS! into C2 nor from C2 into C3. Thus up to failures equivalence, we cannot encode a process with an unbounded number of restrictions into one with a bounded number of restrictions, nor one with a bounded number of restrictions into a restriction-free process. As lemmata for the above results we prove that convergence is decidable for C2 and that language equivalence is decidable for C3 but undecidable for C2. As corollary it follows that convergence is decidable for restriction-free CCS. Finally, we show the expressive power of priorities by providing a faithful encoding of RAMs in C4 thus bearing witness to the expressive power of Phillips' priority guards [76]. The second part of this dissertation is devoted to expressiveness of the asynchronous monadic pi-calculus, A [15, 47]. In [70] the authors studied the expressivenessn of persistence in Api [15, 47] wrt weak barbed congruence. The study is incomplete because it ignores divergence. We shall present an expressiveness study of persistence in Api wrt De Nicola and Hennessy's testing scenario which is sensitive to divergence. Following [70],,we consider Api and three sub-languages of it, each capturing one source of persistence: the persistent-input Api-calculus (PIA), the persistent-output Api-calculus (POA) and the persistent Api-calculus (PA). In [70] the authors showed encodings from Api into the semi-persistent calculi (i.e., POA and PIA) correct wrt weak barbed congruence. We show that, under some general conditions related to compositionality of the encoding and preservation of the infinite behaviour, there cannot be an encoding from Api into a (semi)-persistent calculus preserving the must testing semantics. We also prove that convergence and divergence are decidable for POA (and PA). As a consequence there is no encoding preserving and reflecting divergence or convergence from Api into POA (and PA). This study fills a gap on the expressiveness study of persistence in A in [70]

CCS with Priority Guards

It has long been recognised that ordinary process algebra has difficulty dealing with actions of different priority, such as for instance an interrupt action of high priority. Various solutions have been proposed. We introduce a new approach, involving the addition of “priority guards” to the summation operator of Milner’s process calculus CCS. In our approach, priority is unstratified, meaning that actions are not assigned fixed levels, so that the same action can have different priority depending where it appears in a program. An important feature is that, unlike in other unstratified accounts of priority in CCS (such as that of Camilleri and Winskel), we can treat inputs and outputs symmetrically. We introduce the new calculus, give examples, develop its theory (including bisimulation, equational laws and logics), and compare it with existing approaches

CCS with Priority Guards

. It has long been recognised that ordinary process algebra has difficulty dealing with actions of different priority, such as for instance an interrupt action of high priority. Various solutions have been proposed. We introduce a new approach, involving the addition of "priority guards" to the summation operator of Milner's process calculus CCS. In our approach, priority is unstratified, meaning that actions are not assigned fixed levels, so that the same action can have different priority depending where it appears in a program. An important feature is that, unlike in other unstratified accounts of priority in CCS (such as that of Camilleri and Winskel), we can treat inputs and outputs symmetrically. We introduce the new calculus, give examples, develop its theory (including bisimulation, equational laws and logics), and compare it with existing approaches. 1. INTRODUCTION It has long been recognised that ordinary process algebra [Mil99, Hoa85, BK84] has difficulty dealing with actio..