On Boundedness in Depth in the π-Calculus ⋆

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 .

[1]  Graham Higman,et al.  Ordering by Divisibility in Abstract Algebras , 1952 .

[2]  Robin Milner,et al.  Flowgraphs and Flow Algebras , 1979, JACM.

[3]  Robin Milner,et al.  Concurrent Processes and Their Syntax , 1979, JACM.

[4]  Alain Finkel,et al.  Reduction and covering of infinite reachability trees , 1990, Inf. Comput..

[5]  Annegret Habel,et al.  Hyperedge Replacement: Grammars and Languages , 1992, Lecture Notes in Computer Science.

[6]  Mads Dam.  Model Checking Mobile Processes , 1993, CONCUR.

[7]  Joost Engelfriet,et al.  Multisets and Structural Congruence of the pi-Calculus with Replication , 1999, Theor. Comput. Sci..

[8]  Parosh Aziz Abdulla,et al.  Algorithmic Analysis of Programs with Well Quasi-ordered Domains , 2000, Inf. Comput..

[9]  Davide Sangiorgi,et al.  Communicating and Mobile Systems: the π-calculus, , 2000 .

[10]  Philippe Schnoebelen,et al.  Well-structured transition systems everywhere! , 2001, Theor. Comput. Sci..

[11]  Joost Engelfriet,et al.  Structural inclusion in the pi-calculus with replication , 2001, Theor. Comput. Sci..

[12]  Roberto M. Amadio,et al.  On Decidability of the Control Reachability Problem in the Asynchronous pi-Calculus , 2002, Nord. J. Comput..

[13]  Marco Pistore,et al.  A model-checking verification environment for mobile processes , 2003, TSEM.

[14]  Luís Caires.  Behavioral and Spatial Observations in a Logic for the pi-Calculus , 2004, FoSSaCS.

[15]  Joost Engelfriet,et al.  A new natural structural congruence in the pi-calculus with replication , 2004, Acta Informatica.

[16]  Davide Sangiorgi,et al.  Ensuring termination by typability , 2006, Inf. Comput..

[17]  Raheel Ahmad,et al.  The π-Calculus: A theory of mobile processes , 2008, Scalable Comput. Pract. Exp..

[18]  Roland Meyer,et al.  A theory of structural stationarity in the π-Calculus , 2009, Acta Informatica.