Decidability of Behavioral Equivalences in Process Calculi with Name Scoping [chapter]

Chaodong He, Yuxi Fu, Hongfei Fu
2012 Lecture Notes in Computer Science  
Process calculi are usually Turing complete. The known proofs of Turing completeness share the same guideline that counting is represented as the nesting of suitable components. In the name-passing calculi, the encodings of counter depend on the existence of local channels and some degrees of name-passing capabilities. In the setting of CCS-like calculi, there are several Turing complete variants in which local channels are provided by the localization operation while name-passing capabilities
more » ... re partly obtained by an explicit operation such as parametric definition or relabeling, or by an implicit dynamic-scoping recursion. A fundamental problem in the area of system verification is that of equivalence (or preorder) checking. In concurrency theory these are the problems of deciding whether two given processes are behaviorally equal, or whether one process is behavioral close to the other. Among these equivalences (or preorders), bisimilarity (or similarity) plays a prominent role. This paper explores the decidability issues of bisimilarity/similarity checking problems for various subcalculi of CCS classified by different name scoping rules, in which the capability of producing and manipulating local channels becomes weaker and weaker. These decidability results contribute to the understanding of the way productions and mobilities of local channels affect the expressiveness. The seven subcalculi of CCS studied in this paper are given in Fig. 1 . In the diagram an arrow ' / / ' indicates the sub-language relationship. These seven subcalculi are further divided into four classes in which the scoping rules of local channel names are weakened gradually. The first class contains CCS Pdef , the full CCS with parametric definition (but without relabeling), which is known to be Turing complete. In CCS Pdef process copies can be nested at arbitrary depth by the name-passing capability offered by parametric definition. Turing completeness implies that all behavioral equivalences and preorders for CCS Pdef are undecidable. The second class contains CCS µ and CCS ! . These two subcalculi have the power of producing new local channels but do not have the power of passing names around. In both models the infinite behaviors are specified by (static scoping) recursion and replication respectively. They are not Turing complete because they are not expressive enough to define the process Counter. For the readers unfamiliar with the static scoping recursion, we give the following illustration. Static scoping and dynamic scoping are different ways of manipulating local names when unfolding recursions. When a process is defined as P def = µX.(a | (a)(a | X)), the static scoping requires that the local a and the
doi:10.1007/978-3-642-29320-7_19 fatcat:itbbqzaci5eg3mwh4rkzhnztp4