Abstract
We formulate the GENERALIZED PATTERN MATCHING problem, a natural extension of string searching capturing regularities across scale. The special case of UNAVOIDABILITY TESTING is ob- tained for pure generalized patterns by fixing an appropriate family of text strings - the Zimin words. We investigate the complexity of this restricted decision problem. Although the efficiency of standard string searching is well-known, determining the occurrence of generalized pat- terns in Zimin words does not appear so tractable. We provide an expo- nential lower bound on any algorithmic decision procedure relying exclu- sively on the equivalent deletion sequence characterization of unavoid- able patterns. We also demonstrate that the four other known necessary conditions are not sufficient to decide pattern unavoidability.
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© 2001 Springer-Verlag Berlin Heidelberg
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Heitsch, C.E. (2001). Generalized Pattern Matching and the Complexity of Unavoidability Testing. In: Amir, A. (eds) Combinatorial Pattern Matching. CPM 2001. Lecture Notes in Computer Science, vol 2089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48194-X_20
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DOI: https://doi.org/10.1007/3-540-48194-X_20
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