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Eliminating Recursion from Monadic Datalog Programs on Trees

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Mathematical Foundations of Computer Science 2015 (MFCS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9234))

Abstract

We study the problem of eliminating recursion from monadic datalog programs on trees with labels taken from an infinite alphabet. We show that the boundedness problem, i.e., determining whether a datalog program is equivalent to some nonrecursive one is undecidable but the decidability is regained if the descendant relation is disallowed. Under similar restrictions we obtain decidability of the problem of equivalence to a given nonrecursive program. We investigate the connection between these two problems in more detail.

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Notes

  1. 1.

    One could consider a definition allowing additionally nodes connected by the equality relation but we expect that this would be as hard as the disconnected case e.g. the main problem we leave open in Sect. 3, the equivalence of child-only non-linear programs, becomes undecidable by the results of [18] for boolean queries.

  2. 2.

    In [18] the non-linear case required an additional exponential blow-up. However, the improvement of complexity is not caused by considering unary instead of boolean queries. It is easy to see that Theorem 1 holds also in the boolean case.

  3. 3.

    Indeed, the main idea of the undecidability proof is to use the UCQ \(\mathcal Q\) to find errors in the run of a Turing machine encoded by the program \(\mathcal P\). If the nonrecursive query \(\mathcal Q\) is unary it can only find errors close to the node X, such that \(\mathcal P(X)\).

  4. 4.

    Observe that we are only interested in the output on the goal predicate. This is why the property we consider is sometimes called the predicate boundedness [17].

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Acknowledgments

We are grateful to Anca Muscholl, Pierre Bourhis and Filip Murlak for helpful discussions and constructive comments that lead to a great improvement of the presentation of this paper. The first and third authors were supported by Poland’s National Science Center grant 2013/09/N/ST6/01170, the second author was supported by Poland’s National Science Center grant 2013/11/D/ST6/03075.

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Authors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Filip Mazowiecki, Joanna Ochremiak & Adam Witkowski

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  1. Filip Mazowiecki
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  2. Joanna Ochremiak
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  3. Adam Witkowski
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Correspondence to Filip Mazowiecki .

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Editors and Affiliations

  1. Università di Roma "Tor Vergata", Rome, Italy

    Giuseppe F Italiano

  2. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

  3. University of Edinburgh, Edinburgh, United Kingdom

    Donald T. Sannella

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Mazowiecki, F., Ochremiak, J., Witkowski, A. (2015). Eliminating Recursion from Monadic Datalog Programs on Trees. In: Italiano, G., Pighizzini, G., Sannella, D. (eds) Mathematical Foundations of Computer Science 2015. MFCS 2015. Lecture Notes in Computer Science(), vol 9234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48057-1_31

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  • DOI: https://doi.org/10.1007/978-3-662-48057-1_31

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