On Boundedness in Depth in the π-Calculus⋆
نویسنده
چکیده
We investigate the class PBD of π-Calculus processes that are bounded in the function depth. First, we show that boundedness in depth has an intuitive characterisation when we understand processes as graphs: a process is bounded in depth if and only if the length of the simple paths is bounded. The proof is based on a new normal form for the π-Calculus called anchored fragments. Using this concept, we then show that processes of bounded depth have well-structured transition systems (WSTS). As a consequence, the termination problem is decidable for this class of processes. The instantiation of the WSTS framework employs a new well-quasi-ordering for processes in PBD .
منابع مشابه
Bounds on Mobility
We study natural semantic fragments of the π-calculus: depthbounded processes (there is a bound on the longest communication path), breadth-bounded processes (there is a bound on the number of parallel processes sharing a name), and name-bounded processes (there is a bound on the number of shared names). We give a complete characterization of the decidability frontier for checking if a π-calcul...
متن کاملA Type System for proving Depth Boundedness in the pi-calculus
The depth-bounded fragment of the π-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system, parameterised over a finite forest, that formalises name usage by π-terms in a manner that respects the forest. Type checking is decidable and type inference is compu...
متن کاملDepth Boundedness in Multiset Rewriting Systems with Name Binding
In this paper we consider ν-MSR, a formalism that combines the two main existing approaches for multiset rewriting, namely MSR and CMRS. In ν-MSR we rewrite multisets of atomic formulae, in which some names may be restricted. ν-MSR are Turing complete. In particular, a very straightforward encoding of π-calculus process can be done. Moreover, pν-PN, an extension of Petri nets in which tokens ar...
متن کاملUsing Session Types for Reasoning About Boundedness in the Pi-Calculus
The classes of depth-boundedand name-bounded processes are fragments of the π-calculus for which some of the decision problems that are undecidable for the full calculus become decidable. P is depth-bounded at level k if every reduction sequence for P contains successor processes with at most k active nested restrictions. P is name-bounded at level k if every reduction sequence for P contains s...
متن کاملMultiset rewriting for the verification of depth-bounded processes with name binding
We combine the two existing approaches to the study of concurrency by means of multiset rewriting: multiset rewriting with existential quantification (MSR) and constrained multiset rewriting. We obtain ν-MSR, where we rewrite multisets of atomic formulae, in which terms can only be pure names, where some names can be restricted. We consider the subclass of depth-bounded ν-MSR, for which the int...
متن کامل