Anca Muscholl

Message Sequence Graphs and Decision Problems on Mazurkiewicz Traces

Message sequence chEirts (MSC) are a graphical specification language widely used for designing communication protocols. Our starting point are two decision problems concerning the correctness and the consistency of a design based by MSC graphs. Both problems are shown to be undecidable, in general. Using a natural connectivity assumption from Mazurkiewicz trace theory we show both problems to be EXPSPACE-complete for locally synchronized graphs. The results are based on new complexity results for star-connected rational trace languages.

Deciding Properties for Message Sequence Charts

Message sequence charts (MSC) are commonly used in designing communication systems. They allow describing the communication skeleton of a system and can be used for finding design errors. First, a specification formalism that is based on MSC graphs, combining finite message sequence charts, is presented. We present then an automatic validation algorithm for systems described using the message sequence charts notation. The validation problem is tightly related to a natural language-theoretic problem over semi-traces (a generalization of Mazurkiewicz traces, which represent partially ordered executions). We show that a similar and natural decision problem is undecidable.

Logical Definability on Infinite Traces

The main results of the present paper are the equivalence of monadic second order logic and recognizability for real trace languages, and that first order definable, star-free, and aperiodic real trace languages form the same class of languages. This generalizes results on infinite words [Tho90a, for an overview] and on finite traces [Tho90b, GRS91] to infinite traces. It closes the last gap in the different characterizations of recognizable infinitary trace languages.

Deterministic asynchronous automata for infinite traces

This paper shows the equivalence between the family of recognizable languages over infinite traces and the family of languages which are recognized by deterministic asynchronous cellular Muller automata. We thus give a proper generalization of McNaughtons Theorem from infinite words to infinite traces. Thereby we solve one of the main open problems in this field. As a special case we obtain that every closed (w.r.t. the independence relation) word language is accepted by someI-diamond deterministic Muller automaton.

A note on the commutative closure of star-free languages

We show that the commutative closure of a star-free language is either star-free or not regular anymore. Actually, this property is shown to hold exactly for the closure with respect to a partial commutation corresponding to a transitive dependence relation. Moreover, the question whether the closure of a star-free language remains star-free is decidable precisely for transitive partial commutation relations.

On the Complementation of Büchi Asynchronous Cellular Automata

We present a subset automaton construction for asynchronous cellular automata. This provides an answer to the problem of direct determinization for asynchronous cellular automata for finite traces, which has been open for several years. We use the subset automaton construction in order to extend Klarlunds progress measure technique of complementation to non-deterministic asynchronous cellular Buchi automata for infinite traces. Our automaton for the complement (as well as the subset automaton) has (2^{O(N^{left| Sigma right|} )} ) global states.

Matching Specifications for Message Sequence Charts

Message sequence charts (MSC) are widely used in the early design of communication protocols. They allow describing the communication skeleton of a system. We consider a basic verification task for hierarchical MSCs, the matching problem via MSC templates. We characterize the complexity of checking properties which are expressible by and-or templates, resp. by LTL formulas. Both problems are shown to be PSPACE-complete.

Computing ε-free NFA from regular expressions in O(n log2(N)) time

The standard procedure to transform a regular expression to an e-free NFA yields a quadratic blow-up of the number of transitions. For a long time this was viewed as an unavoidable fact. Recently Hromkovic et.al. [5] exhibited a construction yielding e-free NFA with O(n log2(n)) transitions. A rough estimation of the time needed for their construction shows a cubic time bound. The known lower bound is Ω(n log(n)). In this paper we present a sequential algorithm for the construction described in [5] which works in time O(n log(n) + size of the output). On a CREW PRAM the construction is possible in time O(log(n)) using O(n + (size of the output)/log(n)) processors.

Solving Trace Equations Using Lexicographical Normal Forms

Very recently, the second author showed that the question whether an equation over a trace monoid has a solution or not is decidable [11,12]. In the original proof this question is reduced to the solvability of word equations with constraints, by induction on the size of the commutation relation. In the present paper we give another proof of this result using lexicographical normal forms. Our method is a direct reduction of a trace equation system to a word equation system with regular constraints, using a new result on lexicographical normal forms.

On codings of traces

The paper solves the main open problem of [BFG94]. We show that given two dependence alphabets (σ, D) and (σ′, D′), it is decidable whether there exists a strong coding h: M(σ, D)→M(σ′, D′) between the associated trace monoids. In fact, we show that the problem is NP-complete. (A coding is an injective homomorphism, it is strong if independent letters are mapped to independent traces.) We exhibit an example of trace monoids where a coding between them exists, but no strong coding. The decidability of codings remains open, in general. We have a lower and an upper bound, which show both to be strict. We further discuss encodings of free products of trace monoids and give almost optimal constructions.