Algorithms for approximate string matching
Information and Control
Fast string matching with k-differences
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Machine models and simulations
Handbook of theoretical computer science (vol. A)
Reasoning about strings in databases
PODS '94 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Text algorithms
ACM SIGMOD Record
Counting quantifiers, successor relations, and logarithmic space
Journal of Computer and System Sciences - special issue on complexity theory
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
SQL: 1999, formerly known as SQL3
ACM SIGMOD Record
A fast bit-vector algorithm for approximate string matching based on dynamic programming
Journal of the ACM (JACM)
Discovering Patterns and Subfamilies in Biosequences
Proceedings of the Fourth International Conference on Intelligent Systems for Molecular Biology
Approximate Pattern Matching is Expressible in Transitive Closure Logic
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
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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 show how to adapt the formalisms to allow individual costs for the editing operations, and consider music information retrieval (MIR) as a case study.We believe that in the general case k-differences is not expressible in FO(DTC). However, we show that proving this is at least as hard as separating LOGSPACE from NLOGSPACE. On the other hand, we show that if k is fixed, the k-differences problem can be expressed by an FO(DTC) formula.