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Motivated by reasoning tasks for XML languages, the satisfiability problem of logics on <i>data trees</i> is investigated. The nodes of a data tree have a <i>label</i> from a finite set and a <i>data value</i> from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed(More)
— In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the two-variable first-order logic FO 2 (∼,<,+1) is decidable over finite and over(More)
Message sequence charts (MSC) are a graphical speciica-tion 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(More)
In a <i>data word</i> each position carries a label from a finite alphabet and a data value from some infinite domain. This model has been already considered in the realm of semistructured data, timed automata, and extended temporal logics. This article shows that satisfiability for the two-variable fragment FO<sup>2</sup>(&sim;,&lt;,+1) of first-order(More)
The paper solves the main open problem of [BFG94]. We show that given two dependence alphabets (Σ, D) and (Σ , D), it is de-cidable 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(More)
We consider three natural classes of infinite-state HMSCs: globally-cooperative, locally-cooperative and local-choice HMSCs. We show first that model-checking for globally-cooperative and locally-cooperative HMSCs is of the same complexity as for the class of finite state HMSCs. Surprisingly, model-checking local-choice HMSCs turns out to be exponentially(More)