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- Diego Figueira, Santiago Figueira, Sylvain Schmitz, Philippe Schnoebelen
- 2011 IEEE 26th Annual Symposium on Logic in…
- 2011

Dickson's Lemma is a simple yet powerful tool widely used in decidability 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)

- Pablo Barceló, Diego Figueira, Leonid Libkin
- 2012 27th Annual IEEE Symposium on Logic in…
- 2012

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)

- Diego Figueira
- PODS
- 2009

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)

- Diego Figueira, Luc Segoufin
- MFCS
- 2009

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
- Logical Methods in Computer Science
- 2012

- Diego Figueira, Luc Segoufin
- STACS
- 2011

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)

- Diego Figueira
- 2010

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

- Carlos Areces, Diego Figueira, Santiago Figueira, Sergio Mera
- WoLLIC
- 2008

Taking as inspiration the hybrid logic HL(↓), we introduce a new family of logics that we call memory logics. In this article we present in detail two interesting members of this family defining their formal syntax and semantics. We then introduce a proper notion of bisimulation and investigate their expressive power (in comparison with modal and hybrid… (More)

- Diego Figueira
- ICDT
- 2010

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)