A Semiring-Based Trace Semantics for Processes with Applications to Information Leakage Analysis

Abstract. We propose a framework for reasoning about program security building on language-theoretic and coalgebraic concepts. The behaviour of a system is viewed as a mapping from traces of high (unobservable) events to low (observable) events: the less the degree of dependency of low events on high traces, secure the system. We take the abstract view that low events are drawn from a generic semiring, where they can be combined using product and sum operations; throughout the paper, we provide instances of this framework, obtained by concrete instantiations of the underlying semiring. We specify systems via a simple process calculus, whose semantics is given as the unique homomorphism from the calculus into the set of behaviours, i.e. formal power series, seen as a final coalgebra. We provide a compositional semantics for the calculus in terms of rational operators on formal power series and show that the final and the compositional semantics coincide.

• Type: Journal
• Year: 2010
• Where: IFIPTCS
• Authors: Michele Boreale, David Clark, Daniele Gorla
• Keywords: Calculus, Compositional Semantics, Formal Power Series, IFIPTCS 2010, Theoretical Computer Science