Abstract
The problem of many-to-one unification, i.e. a simultaneous weak unification of pattern terms against all subterms of a target term, is studied for linear terms. Two algorithms proposed in [10] generalize either the many-to-one tree pattern matching algorithm [5] based on the path counting principle or the rooted many-to-one tree pattern unification algorithm [11] based on the pattern elimination principle. In both cases, the asymptotical worst-case time complexity of tree pattern unification is quadratic as in the special case of tree pattern matching. However, the expected time complexity of the “patterneliminating” algorithm is linear according to the size of the input. In this paper we improve the worst-case time bound result by designing an O(nm 0.75 logk m) algorithm for finding all occurrences of a pattern term-tree of the size m in a target term-tree of the size n, for some fixed k. The algorithm is extensible to many-to-one version of tree pattern unification problem and is also suitable for applications with dynamically changing set of patterns.
This research has been partially supported by the EC Cooperative Action IC 1000 (project ALTEC: Algorithms for Future Technologies) and by the Slovak GAV project 1/1447/94.
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© 1996 Springer-Verlag Berlin Heidelberg
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Ružička, P. (1996). Efficient tree pattern unification. In: Jeffery, K.G., Král, J., Bartošek, M. (eds) SOFSEM'96: Theory and Practice of Informatics. SOFSEM 1996. Lecture Notes in Computer Science, vol 1175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0037425
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DOI: https://doi.org/10.1007/BFb0037425
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