CCS with Replication in the Chomsky Hierarchy: The Expressive Power of Divergence

Jesus Aranda (1, 2) , Cinzia Di Giusto (3) , Mogens Nielsen (4) , Frank Valencia (1)

1 COMETE - Concurrency, Mobility and Transactions
2 EISC - Escuela de Ingenieria de Sistemas y Computacion
3 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna
4 Aarhus University [Aarhus]

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 .

Mots clés: Expressiveness; Process calculi; CCS

Domaines: Informatique et langage [cs.CL]

Jesus Aranda, Cinzia Di Giusto, Mogens Nielsen, Frank Valencia. CCS with Replication in the Chomsky Hierarchy: The Expressive Power of Divergence. 5th Asian Symposium on Programming Languages and Systems (APLAS'07), Nov 2007, Singapore, Singapore. pp.383-398, ⟨10.1007/978-3-540-76637-7_26⟩. ⟨inria-00201547⟩