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

Jesús Aranda, Cinzia Di Giusto, Mogens Nielsen, Frank D. Valencia
2007 Lecture Notes in Computer Science  
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
more » ... oding 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 . The work of Jesús Aranda has been supported by COLCIENCIAS (Instituto Colombiano para el Desarrollo de la Ciencia y la Tecnología "Francisco José de Caldas") and INRIA Futurs.
doi:10.1007/978-3-540-76637-7_26 fatcat:wljwhmgttzcqzin7n34v6c66ee