## Corrections to some errors in my papers

Carlos Buil-Aranda, Marcelo Arenas, Oscar Corcho and Axel Polleres. Federating Queries in SPARQL1.1: Syntax, Semantics and Evaluation. Journal of Web Semantics 18(1):1-17, 2013.

If *P* is a graph pattern of the form *(GRAPH c
Q)* with *c* in *I*, then
is defined as
if *c* does not belong to *names(DS)* (see Figure 1). This semantics does not agree with
the official
semantics of the *GRAPH* operator given by the W3C (thanks
to Xiaowang Zhang for pointing this out to us). To solve this problem
has to be defined as
(the empty set of mappings).

Jorge Perez, Marcelo Arenas and Claudio Gutierrez. Semantics and Complexity of SPARQL. ACM Transactions on Database Systems, 34(3), Article 16 (45 pages), 2009.

The following error was introduced by the journal during the editing/proofing stages. Second line of page 6:

should be replaced by:

Thanks to Andres Letelier for catching this.

Marcelo Arenas, Pablo Barcelo and Leonid Libkin. Regular Languages of Nested Words: Fixed Points, Automata, and Synchronization. In Proceedings of the 34th International Colloquium on Automata, Languages and Programming (ICALP'07), Wroclaw, Poland, volume 4596 of Lecture Notes in Computer Science, pages 888-900, 2007.

The proof of Theorem 3 (and, thus, of Corollary 7) is incorrect. In the journal version of this paper, we provide a corrected proof of the fact that for every alternating NWA, there exists (and can be effectively constructed) an equivalent NWA. More precisely, the following is proved in the journal version of this paper:

Proposition 4.14. For every alternating NWA of size n, there exists (and can be effectively constructed) an equivalent NWA of size:

Jorge Perez, Marcelo Arenas and Claudio Gutierrez. Semantics and Complexity of SPARQL. In Proceedings of the 5th International Semantic Web Conference (ISWC'06), Athens, GA, USA, volume 4273 of Lecture Notes in Computer Science, pages 30-43, Springer, 2006.

Point (3) of Proposition 1 is incorrect (thanks to Michael Schmidt for pointing this out to us). It states that the following equivalence holds in general:

As a consequence, the proof that shows that every SPARQL pattern is equivalent to a pattern in UNION normal is not correct. Nevertheless, we provide in the journal version of this paper a new proof of this fact, which does not use the previous incorrect equivalence.

Marcelo Arenas, Leopoldo Bertossi and Michael Kifer. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In Proceedings of the 6th International Conference on Rules and Objects in Databases (DOOD'00), London, UK, volume 1861 of Lecture Notes in Artificial Intelligence, pages 926-941. Springer, 2000.

Third line of Proposition 3 (page 940): *NP-complete*
must be replaced by *coNP-complete*.