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Dashed Strings and the Replace(-all) Constraint

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Principles and Practice of Constraint Programming (CP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12333))

Abstract

Dashed strings are a formalism for modelling the domain of string variables when solving combinatorial problems with string constraints. In this work we focus on (variants of) the Replace constraint, which aims to find the first occurrence of a query string in a target string, and (possibly) replaces it with a new string. We define a Replace propagator which can also handle Replace-Last (for replacing the last occurrence) and Replace-All (for replacing all the occurrences). Empirical results clearly show that string constraint solving can draw great benefit from this approach.

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Notes

  1. 1.

    \(\sqsubseteq \) is not defined as \(X \sqsubseteq Y \iff \gamma (X) \subseteq \gamma (Y)\) because otherwise \(\sqsubseteq \) would be a pre-order but not a partial order in general, e.g., if \(\lambda =2\) then \(X = \{a,b,c\}^{0,2}\) and \(Y = \{a,b\}^{0,2}\{b,c\}^{0,2}\{a,c\}^{0,2}\) are such that \(\gamma (X) \subseteq \gamma (Y)\) and \(\gamma (Y) \subseteq \gamma (X)\) so \(X \sqsubseteq Y\) and \(Y \sqsubseteq X\) but \(X \ne Y\).

  2. 2.

    In [7] it was called Sweep to distinguish it the Cover equation algorithm.

  3. 3.

    Push and Stretch are not dual. For example, when incompatible blocks are found, Push moves on (Fig. 2, line 9) while Stretch returns (Fig. 3, line 13).

  4. 4.

    In [5] the order of Replace arguments is different. In this paper we change the notation to be consistent with SMT-LIB specifications.

  5. 5.

    For simplicity, in Fig. 4 we assume that, when \(\textsc {Equate} (X,Y) \ne \bot \), \(\textsc {Equate} (X,Y)\) modifies its arguments instead of returning a pair of refined dashed strings \((X',Y')\).

  6. 6.

    We used a Ubuntu 15.10 machine with 16 GB of RAM and 2.60 GHz Intel® i7 CPU. The benchmarks and the source code of the experiments is available at https://bitbucket.org/robama/exp_cp_2020.

  7. 7.

    Since optimization is not a native feature for CVC4 we implemented it by iteratively solving decision problems with refined objective bounds.

  8. 8.

    This work is supported by Australian Research Council through Linkage Project Grant LP140100437 and Discovery Early Career Researcher Award DE160100568.

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Authors and Affiliations

  1. University of Bologna, Bologna, Italy

    Roberto Amadini

  2. Monash University, Melbourne, VIC, Australia

    Graeme Gange & Peter J. Stuckey

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  1. Roberto Amadini
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  2. Graeme Gange
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Correspondence to Roberto Amadini .

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  1. Insight Centre for Data Analytics, School for Computer Science and Information Technology, University College Cork, Cork, Ireland

    Helmut Simonis

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Amadini, R., Gange, G., Stuckey, P.J. (2020). Dashed Strings and the Replace(-all) Constraint. In: Simonis, H. (eds) Principles and Practice of Constraint Programming. CP 2020. Lecture Notes in Computer Science(), vol 12333. Springer, Cham. https://doi.org/10.1007/978-3-030-58475-7_1

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  • DOI: https://doi.org/10.1007/978-3-030-58475-7_1

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