Jesper G. Henriksen

A theory of regular MSC languages

Message sequence charts (MSCs) are an attractive visual formalism widely used to capture system requirements during the early design stages in domains such as telecommunication software. It is fruitful to have mechanisms for specifying and reasoning about collections of MSCs so that errors can be detected even at the requirements level. We propose, accordingly, a notion of regularity for collections of MSCs and explore its basic properties. In particular, we provide an automata-theoretic characterization of regular MSC languages in terms of finite-state distributed automata called bounded message-passing automata. These automata consist of a set of sequential processes that communicate with each other by sending and receiving messages over bounded FIFO channels. We also provide a logical characterization in terms of a natural monadic second-order logic interpreted over MSCs. A commonly used technique to generate a collection of MSCs is to use a hierarchical message sequence chart (HMSC). We show that the class of languages arising from the so-called bounded HMSCs constitute a proper subclass of the class of regular MSC languages. In fact, we characterize the bounded HMSC languages as the subclass of regular MSC languages that are finitely generated.

Mona: Monadic Second-Order Logic in Practice

The purpose of this article is to introduce Monadic Second-order Logic as a practical means of specifying regularity. The logic is a highly succinct alternative to the use of regular expressions. We have built a tool MONA, which acts as a decision procedure and as a translator to finite-state automata. The tool is based on new algorithms for minimizing finite-state automata that use binary decision diagrams (BDDs) to represent transition functions in compressed form. A byproduct of this work is an algorithm that matches the time but improves the space of Sieling and Wegeners algorithm to reduce OBDDs in linear time.

A Product Version of Dynamic Linear Time Temporal Logic

We present here a linear time temporal logic which simultaneously extends LTL, the propositional temporal logic of linear time, along two dimensions. Firstly, the until operator is strengthened by indexing it with the regular programs of propositional dynamic logic (PDL). Secondly, the core formulas of the logic are decorated with names of sequential agents drawn from fixed finite set. The resulting logic has a natural semantics in terms of the runs of a distributed program consisting of a finite set of sequential programs that communicate by performing common actions together. We show that our logic, denoted DLTL⊗, admits an exponential time decision procedure. We also show that DLTL⊗ is expressively equivalent to the so called regular product languages. Roughly speaking, this class of languages is obtained by starting with synchronized products of (ω-)regular languages and closing under boolean operations. We also sketch how the behaviours captured by our temporal logic fit into the framework of labelled partial orders known as Mazurkiewicz traces.

Distributed Versions of Linear Time Temporal Logic: A Trace Perspective

In this paper we have attempted an overview of linear time temporal logics interpreted over traces. We have mainly concentrated on the satisfiability and model checking problems as well as expressiveness issues. The problem of axiomatizing these logics seems to be a non-trivial task. Some partial results may be found in [39]. In [34] the authors present proof rules for the logic ISTL with a trace semantics together with a relative expressive completeness result. Reisig has also developed a kit of proof rules for a version of UNITY logic [40, 41]. The models of this logic are the non-sequential processes of a net system and the proof rules are mainly designed to help reason about distributed algorithms modelled using net systems.

An Expressive Extension of TLC

A temporal logic of causality (TLC) was introduced by Alur, Penczek and Peled in [1]. It is basically a linear time temporal logic interpreted over Mazurkiewicz traces which allows quantification over causal chains. Through this device one can directly formulate causality properties of distributed systems. In this paper we consider an extension of TLC by strengthening the chain quantification operators. We show that our logic TLC* adds to the expressive power of TLC. We do so by defining an Ehrenfeucht-Fraisse game to capture the expressive power of TLC. We then exhibit a property and by means of this game prove that the chosen property is not definable in TLC. We then show that the same property is definable in TLC*. We prove in fact the stronger result that TLC* is expressively stronger than TLC exactly when the dependency relation associated with the underlying trace alphabet is not transitive.