Abstract
A remarkable result in [4] shows that in spite of its being less expressive than CCS w.r.t. weak bisimilarity, CCS! (a CCS variant where infinite behavior is specified by using replication rather than recursion) is Turing powerful. This is done by encoding Random Access Machines (RAM) 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 paper we 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 show that the languages generated by termination-preserving CCS! processes are Type 1 .
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References
Baeten, J.C.M., Corradini, F.: Regular expressions in process algebra. In: LICS 2005, pp. 12–19. IEEE Computer Society Press, Washington, DC, USA (2005)
Burkart, O., Caucal, D., Moller, F., Steffen, B.: Verification on infinite structures ch. 9, pp. 545–623. Elsevier, North-Holland (2001)
Busi, N., Gabbrielli, M., Zavattaro, G.: Replication vs. recursive definitions in channel based calculi. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 133–144. Springer, Heidelberg (2003)
Busi, N., Gabbrielli, M., Zavattaro, G.: Comparing recursion, replication, and iteration in process calculi. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 307–319. Springer, Heidelberg (2004)
Giambiagi, P., Schneider, G., Valencia, F.D.: On the expressiveness of infinite behavior and name scoping in process calculi. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 226–240. Springer, Heidelberg (2004)
Huttel, H., Srba, J.: Recursion vs. replication in simple cryptographic protocols. In: Vojtáš, P., Bieliková, M., Charron-Bost, B., Sýkora, O. (eds.) SOFSEM 2005. LNCS, vol. 3381, pp. 175–184. Springer, Heidelberg (2005)
Kanellakis, P.C., Smolka, S.A.: CCS expressions finite state processes, and three problems of equivalence. Inf. Comput. 86(1), 43–68 (1990)
Milner, R.: A complete inference system for a class of regular behaviours. J. Comput. Syst. Sci. 28(3), 439–466 (1984)
Milner, R.: Communication and Concurrency. International Series in Computer Science. Prentice Hall, Englewood Cliffs (1989) SU Fisher Research 511/24
Milner, R.: Communicating and Mobile Systems: the π-calculus. Cambridge University Press, Cambridge (1999)
Minsky, M.: Computation: finite and infinite machines. Prentice-Hall, Englewood Cliffs (1967)
Nielsen, M., Palamidessi, C., Valencia, F.: On the expressive power of concurrent constraint programming languages. In: PPDP 2002, pp. 156–167. ACM Press, New York (2002)
Palamidessi, C., Valencia, F.D.: Recursion vs replication in process calculi: Expressiveness. Bulletin of the EATCS 87, 105–125 (2005)
Parrow, J.: Trios in concert. In: Plotkin, G., Stirling, C., Tofte, M. (eds.) Proof, Language and Interaction: Essays in Honour of Robin Milner, pp. 621–637. MIT Press, Cambridge (2000)
Sangiorgi, D., Walker, D.: PI-Calculus: A Theory of Mobile Processes. Cambridge University Press, New York (2001)
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Aranda, J., Di Giusto, C., Nielsen, M., Valencia, F.D. (2007). CCS with Replication in the Chomsky Hierarchy: The Expressive Power of Divergence. In: Shao, Z. (eds) Programming Languages and Systems. APLAS 2007. Lecture Notes in Computer Science, vol 4807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76637-7_26
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DOI: https://doi.org/10.1007/978-3-540-76637-7_26
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