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In this paper, a process algebra that incorporates expliclt representations of successful termination, deadlock, and divergence is introduced and its semantic theory is analyzed. Both an operational and a denotational semantics for the language is given and it is shown that they agree. The operational theory N based upon a suitable adaptation of the notion of bisimulation preorder. The denotational semantics forthelanguage isgiven interms of theinitial continuous algebra that satisfiesa set of equations E, CI~. It is shown that C'IE is fully abstract with respect to our choice of behavioral preorder. Several results ofindependent interest are obtained; namely, the finite approximability of the behavioral preorder and a partial completeness result for the set of equations E with respect to the preorder.

The importance of giving precise semantics to programming and specification<br />languages was recognized since the sixties with the development of the<br />first high-level programming languages (cf. e.g. [30, 206] for some early accounts).<br />The use of operational semantics - i.e. of a semantics that explicitly<br />describes how programs compute in stepwise fashion, and the possible<br />state-transformations they perform - was already advocated by McCarthy<br />in [147], and elaborated upon in references like [142, 143]. Examples of full-blown<br />languages that have been endowed with an operational semantics are<br />Algol 60 [140], PL/I [173], and CSP [178].

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This paper establishes a comprehensive theory of runtime monitorability for Hennessy-Milner logic with recursion, a very expressive variant of the modal µ-calculus. It investigates the monitorability of that logic with a linear-time semantics and then compares the obtained results with ones that were previously presented in the literature for a branching-time setting. Our work establishes an expressiveness hierarchy of monitorable fragments of Hennessy-Milner logic with recursion in a linear-time setting and exactly identifies what kinds of guarantees can be given using runtime monitors for each fragment in the hierarchy. Each fragment is shown to be complete, in the sense that it can express all properties that can be monitored under the corresponding guarantees. The study is carried out using a principled approach to monitoring that connects the semantics of the logic and the operational semantics of monitors. The proposed framework supports the automatic, compositional synthesis of correct monitors from monitorable properties.

Abstract. We study µHML (a branching-time logic with least and greatest fixpoints) from a runtime verification perspective. We establish which subset of the logic can be verified at runtime and define correct monitor-synthesis algorithms for this subset. We also prove completeness results wrt. these logical subsets that show that no other properties apart from those identified can be verified at runtime.

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