CSPe is a specification language for runtime monitors that can directly express concurrency in a bottom-up manner that composes the system from simpler, interacting components. It includes constructs to explicitly flag failures to the monitor, which unlike deadlocks and livelocks in conventional process algebras, propagate globally and aborts the whole system's execution. Although CSPe has a trace semantics along with an implementation demonstrating acceptable performance, it lacks an operational semantics. An operational semantics is not only more accessible than trace semantics but also indispensable for ensuring the correctness of the implementation. Furthermore, a process algebra like CSPe admits multiple denotational semantics appropriate for different purposes, and an operational semantics is the basis for justifying such semantics' integrity and relevance. In this paper, we develop an SOS-style operational semantics for CSPe, which properly accounts for explicit failures and will serve as a basis for further study of its properties, its optimization, and its use in runtime verification.
The main issue with semantics is the propagation of @math , which entails the negative constraint that normal computation rules apply only if @math -propagation rules do not. Negative premises of the form @math come quite naturally as a means for codifying such constraints, but negative premises are generally quite problematic. A transition relation satisfying negative rules may be not-existent, or non-unique, with no obvious guiding principle (such as minimality) in choosing the right'' one. Some formats do guarantee well-definedness, such as GSOS with the witnessing constraint @cite_2 and @cite_7 . But even then, negative rules tend to betray desirable properties such as compositionality of some forms of bisimulation @cite_4 .
@cite_4 @cite_7 @cite_2
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In this study, we present rule formats for four main notions of bisimulation with silent moves. Weak bisimulation is a congruence for any process algebra defined by WB cool rules; we have similar results for rooted weak bisimulation (Milner''s observational equivalence''''), branching bisimulation, and rooted branching bisimulation. The theorems stating that, say, observational equivalence is an appropriate notion of equality for CCS are corollaries of the results of this paper. We also give sufficient conditions under which equational axiom systems can be generated from operational rules. Indeed, many equational axiom systems appearing in the literature are instances of this general theory. In the concurrent language CCS, two programs are considered the same if they are bisimilar . Several years and many researchers have demonstrated that the theory of bisimulation is mathematically appealing and useful in practice. However, bisimulation makes too many distinctions between programs. We consider the problem of adding operations to CCS to make bisimulation fully abstract. We define the class of GSOS operations, generalizing the style and technical advantages of CCS operations. We characterize GSOS congruence in as a bisimulation-like relation called ready-simulation . Bisimulation is strictly finer than ready simulation, and hence not a congruence for any GSOS language.