NDLI: Approximate pattern matching is expressible in transitive closure logic

Content Provider	IEEE Xplore Digital Library
Author	Lemstrom, K. Hella, L.
Copyright Year	2000
Description	Author affiliation: Dept. of Comput. Sci., Helsinki Univ., Finland (Lemstrom, K.)
Abstract	A sartorial query language facilitates the formulation of queries to a (string) database. One step towards an implementation of such a query language can be taken by defining a logical formalism expressing a known solution for the particular problem at hand. The simplicity of the logic is a desired property because the simpler the logic that the query language is based on, the more efficiently it can be implemented. We introduce a logical formalism for expressing approximate pattern matching. The formalism uses properties of the dynamic programming approach; a minimizing path of a dynamic programming table is expressed by using a formula in an extension of first-order logic (FO). We consider the well-known problems of k mismatches and k differences. Assuming first that k is given as a part of the input, those problems are expressed by using deterministic transitive closure logic (FO(DTC)) and transitive closure logic (FO(TC)), respectively. We believe that in the general case the k differences is not expressible in FO(DTC), and show that solving this question in the affirmative is at least as hard as separating LOGSPACE from NLOGSPACE. We show, however, that if k is fixed, the k differences problem can be expressed by an FO(DTC)formula.
Starting Page	157
Ending Page	167
File Size	358115
Page Count	11
File Format	PDF
ISBN	0769507255
ISSN	10436871
DOI	10.1109/LICS.2000.855764
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2000-06-28
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Pattern matching Database languages Logic programming Multimedia databases Dynamic programming Image retrieval Music information retrieval Image databases Computer science Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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