Bounds on Mobility
We study natural semantic fragments of the π-calculus: depth-bounded 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-calculus process in one subclass belongs to another. Our main construction is a general acceleration scheme for π-calculus processes. Based on this acceleration, we define a Karp and Miller (KM) tree construction for the depth-bounded π-calculus. The KM tree can be used to decide if a depth-bounded process is name-bounded, if a depth-bounded process is breadth-bounded by a constant k, and if a name-bounded process is additionally breadth-bounded. Moreover, we give a procedure that decides whether an arbitrary process is bounded in depth by a given k.
We complement our positive results with undecidability results for the remaining cases. While depth- and name-boundedness are known to be Σ1-complete, we show that breadth-boundedness is Σ2-complete, and checking if a process has a breadth bound at most k is Π1-complete, even when the input process is promised to be breadth-bounded.
Unable to display preview. Download preview PDF.
- 3.Emerson, E.A., Namjoshi, K.S.: On model checking for non-deterministic infinite-state systems. In: LICS, pp. 70–80 (June 1998)Google Scholar
- 6.Finkel, A., Goubault-Larrecq, J.: Forward analysis for WSTS, part I: Completions. In: STACS, pp. 433–444 (2009)Google Scholar
- 11.Meyer, R.: On boundedness in depth in the π-calculus. In: Ausiello, G., Karhumäki, J., Mauri, G., Ong, L. (eds.) IFIP TCS. IFIP, vol. 273, pp. 477–489. Springer, Heidelberg (2008)Google Scholar
- 13.Milner, R.: Communicating and Mobile Systems: the π-Calculus. CUP (1999)Google Scholar
- 16.Sangiorgi, D., Walker, D.: The π-calculus: a Theory of Mobile Processes. CUP (2001)Google Scholar
- 17.Soare, R.I.: Recursively enumerable sets and degrees. Springer (1980)Google Scholar