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
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
Discovering Patterns and Subfamilies in Biosequences
Proceedings of the Fourth International Conference on Intelligent Systems for Molecular Biology
A Fast Bit-Vector Algorithm for Approximate String Matching Based on Dynamic Programming
CPM '98 Proceedings of the 9th Annual Symposium on Combinatorial Pattern Matching
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Design and implementation of a string database query language
Information Systems - Special issue: Data management in bioinformatics
Approximate pattern matching and transitive closure logics
Theoretical 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 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 difference problem can be expressed by an FO(DTC) formula.