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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 LTL1(F), that extends LTL(F) with one register for storing data values for later comparisons. We show that satisfiability over data words of LTL1(F) is already non primitive recursive. We also… (More)

- Diego Figueira
- Logical Methods in Computer Science
- 2012

- Carlos Areces, Diego Figueira, Santiago Figueira, Sergio Mera
- Rew. Symb. Logic
- 2011

We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic HL(↓), for example, can be thought of as a particular case of a memory logic where… (More)

- Diego Figueira
- ArXiv
- 2012

We study the finite satisfiability problem for first order logic with two variables and two binary relations, corresponding to the induced successor relations of two finite linear orders. We show that the problem is decidable in NExpTime.

- Diego Figueira
- LICS
- 2016

The evaluation problem for Conjunctive Queries (CQ) is known to be NP-complete in combined complexity and W[1]-hard in parameterized complexity. However, acyclic CQs and CQs of bounded tree-width can be evaluated in polynomial time in combined complexity and they are fixed-parameter tractable.
We study the problem of whether a CQ can be rewritten into an… (More)

- Stéphane Demri, Diego Figueira, M. Praveen
- 2013 28th Annual ACM/IEEE Symposium on Logic in…
- 2013

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)

- Pablo Barceló, Diego Figueira, Leonid Libkin
- Logical Methods in Computer Science
- 2013

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)