Comparative metric semantics for concurrent Prolog

AbstractThis paper shows the equivalence of two semantics for a version of Concurrent Prolog with non-flat guards: an operational semantics based on a transition system and a denotational semantics which is a metric semantics (the domains are metric spaces). We do this in the following manner. First a uniform language L is considered, that is a language where the atomic actions have arbitrary interpretations. For this language we define an operational and a denotational semantics, and we prove that the denotational semantics is correct with respect to the operational semantics. This result relies on Banach's fixed point theorem. Techniques stemming from imperative languages are used. Then we show how to translate a Concurrent Prolog program to a program in L by selecting certain basic sets for L and then instantiating the interpretation function for the atomic actions. In this way we induce the two semantics for Concurrent Prolog and the equivalence between the two semantics

Parameterized Model Checking of Token-Passing Systems

We revisit the parameterized model checking problem for token-passing systems and specifications in indexed $\textsf{CTL}^\ast \backslash \textsf{X}$. Emerson and Namjoshi (1995, 2003) have shown that parameterized model checking of indexed $\textsf{CTL}^\ast \backslash \textsf{X}$ in uni-directional token rings can be reduced to checking rings up to some \emph{cutoff} size. Clarke et al. (2004) have shown a similar result for general topologies and indexed $\textsf{LTL} \backslash \textsf{X}$, provided processes cannot choose the directions for sending or receiving the token. We unify and substantially extend these results by systematically exploring fragments of indexed $\textsf{CTL}^\ast \backslash \textsf{X}$ with respect to general topologies. For each fragment we establish whether a cutoff exists, and for some concrete topologies, such as rings, cliques and stars, we infer small cutoffs. Finally, we show that the problem becomes undecidable, and thus no cutoffs exist, if processes are allowed to choose the directions in which they send or from which they receive the token.Comment: We had to remove an appendix until the proofs and notations there is cleare

From failure to success: comparing a denotational and a declarative semantics for Horn clause logic

AbstractThe main purpose of the paper is to relate different models for Horn clause logic: operational, denotational, declarative. We study their relationship by contrasting models based on interleaving, on the one hand, to models based on maximal parallelism, on the other. We make use of complete metric spaces as an important mathematical tool, both in defining and in comparing the various models