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We investigate some basic questions about the interaction of regular and rational relations on words. The primary motivation comes from the study of logics for querying graph topology, which have recently found numerous applications. Such logics use conditions on paths expressed by regular languages and relations, but they often need to be extended by… (More)

Dickson's Lemma is a simple yet powerful tool widely used in decidabil-ity proofs, especially when dealing with counters or related data structures in algorithmics, verification and model-checking, constraint solving, logic, etc. While Dickson's Lemma is well-known, most computer scientists are not aware of the complexity upper bounds that are entailed by… (More)

In this work we investigate the satisfiability problem for the logic XPath(↓*, ↓,=), that includes all downward axes as well as equality and inequality tests. We address this problem in the absence of DTDs and the sibling axis. We prove that this fragment is decidable, and we nail down its complexity, showing the problem to be ExpTime-complete.… (More)

In a data word or a data tree each position carries a label from a finite alphabet and a data value from an infinite domain. Over data words we consider the logic LTL ↓ 1 (F), that extends LTL(F) with one register for storing data values for later comparisons. We show that satisfiability over data words of LTL ↓ 1 (F) is already non primitive recursive. We… (More)

- Diego Figueira
- 2010

On decidable automata on data words and data trees in relation to satisfiability of LTL and XPath.

A data tree is a tree whose every node carries a label from a finite alphabet and a datum from some infinite domain. We introduce a new model of automata over unranked data trees with a decidable emptiness problem. It is essentially a bottom-up alternating automaton with one register, enriched with epsilon-transitions that perform tests on the data values… (More)

We consider a fragment of XPath named 'forward-XPath', which contains all descendant and rightwards sibling axes as well as data equality and inequality tests. The satisfiability problem for forward-XPath in the presence of DTDs and even of primary key constraints is shown here to be decidable.
To show decidability we introduce a model of alternating… (More)

We study linear-time temporal logics interpreted over data words with multiple attributes. We restrict the atomic formulas to equalities of attribute values in successive positions and to repetitions of attribute values in the future or past. We demonstrate correspondences between satisfiability problems for logics and reach ability-like decision problems… (More)