On the existence and decidability of unique decompositions of processes in the applied π-calculus (original) (raw)

On Unique Decomposition of Processes in the Applied π-Calculus

Lecture Notes in Computer Science, 2013

Unique decomposition has been a subject of interest in process algebra for a long time (for example in BPP [2] or CCS [10, 12]), as it provides a normal form with useful cancellation properties. We provide two parallel decomposition results for subsets of the Applied π-Calculus: We show that a closed finite process P can be decomposed uniquely into prime factors P i with respect to weak labeled bisimilarity, i.e. such that P ≈ l P 1 |. .. |P n. We also prove that closed normed processes (i.e. processes with a finite shortest trace) can be decomposed uniquely with respect to strong labeled bisimilarity.

A Well-behaved LTS for the Pi-calculus::(Abstract)

Electronic Notes in Theoretical Computer Science, 2007

The pi-calculus and its many variations have received much attention in the literature. We discuss the standard early labelled transition system (lts) and outline an approach which decomposes the system into two components, one of which is presented in detail. The advantages of using the decomposition include a more complete understanding of the treatment of bound outputs in Pi as well as an lts which is more robust with respect to the addition and removal of language features. The present paper serves as an overview of some of the techniques involved and some of the goals of the ongoing work.

Occurrence Counting Analysis for the [pi]-calculus

Electronic Notes in Theoretical Computer Science, 2001

We propose an abstract interpretation-based analysis for automatically proving non-trivial properties of mobile systems of processes. We focus on properties relying on the number of occurrences of processes during computation sequences, such as mutual exclusion and non-exhaustion of resources. We design a non-standard semantics for the π-calculus in order to explicitly trace the origin of channels and to solve efficiently problems set by α-conversion and nondeterministic choices. We abstract this semantics into an approximate one. The use of a relational domain for counting the occurrences of processes allows us to prove quickly and efficiently properties such as mutual exclusion and non-exhaustion of resources. At last, dynamic partitioning allows us to detect some configurations by which no infinite computation sequences can pass.

Occurrence Counting Analysis for the π-calculus

Electronic Notes in Theoretical Computer Science, 2000

We propose an abstract interpretation-based analysis for automatically proving non-trivial properties of mobile systems of processes. We focus on properties relying on the number of occurrences of processes during computation sequences, such as mutual exclusion and non-exhaustion of resources. We design a non-standard semantics for the π-calculus in order to explicitly trace the origin of channels and to solve efficiently problems set by α-conversion and nondeterministic choices. We abstract this semantics into an approximate one. The use of a relational domain for counting the occurrences of processes allows us to prove quickly and efficiently properties such as mutual exclusion and non-exhaustion of resources. At last, dynamic partitioning allows us to detect some configurations by which no infinite computation sequences can pass.

Theory and implementation of a real-time extension to the π-calculus

Formal Techniques for Distributed Systems, 2010

We present a real-time extension to the π-calculus and use it to study a notion of time-bounded equivalence. We introduce the notion of timed compositionality and the associated timed congruence which are useful to reason about the timed behaviour of processes under hard constraints. In addition to this meta-theory we develop an abstract machine for our calculus based on event-scheduling and establish its soundness w.r.t. the given operational semantics. We have built an implementation for a realistic language called kiltera based on this machine.

Final semantics for the π-calculus

Programming Concepts and Methods PROCOMET ’98, 1998

In this paper we discuss nal semantics for the-calculus, a process algebra which models systems that can dynamically change the topology of the channels. We show that the nal semantics paradigm, originated by Aczel and Rutten for CCS-like languages, can be successfully applied also here. This is achieved by suitably generalizing the standard techniques so as to accommodate the mechanism of name creation and the behaviour of the binding operators peculiar to the-calculus. As a preliminary step, we give a higher order presentation of the-calculus using as metalanguage LF, a logical framework based on typed-calculus. Such a presentation highlights the nature of the binding operators and elucidates the rôle of free and bound channels. The nal semantics is de ned making use of this higher order presentation, within a category of hypersets.

On the expressivity of infinite and local behaviour in fragments of the pi-calculus

The pi-calculus [Miln99] 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 (\nu x)P represents a process P with local resource x. The replication !P can be thought of as abbreviating the parallel composition P | P | P .... of an unbounded number of P processes. As for other language-based formalisms (e.g., logic, formal grammars and the lambda-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 ...

A Fully Abstract Model for the π-calculus

Information and Computation, 2002

This paper provides both a fully abstract (domaintheoretic) model for the π-calculus and a universal (set-theoretic) model for the finite π-calculus with respect to strong late bisimulation and congruence. This is done by: considering categorical models, defining a metalanguage for these models, and translating the π-calculus into the metalanguage. A technical novelty of our approach is an abstract proof of full abstraction: The result on full abstraction for the finite π-calculus in the set-theoretic model is axiomatically extended to the whole π-calculus with respect to the domain-theoretic interpretation. In this proof, a central role is played by the description of nondeterminism as a free construction and by the equational theory of the metalanguage.