For a given context-free grammar (CFG) and a finite-state automaton (FA), we tackle the edit-distance problem-the problem of computing the most similar pair of strings in the two respective languages. In particular, we consider three different gap cost models for the edit-distance that are crucial for finding a proper alignment between two bio sequences: The linear, affine and concave models. We design efficient algorithms for the edit-distance between a CFG and an FA under these gap cost models. The time complexity of our algorithm for computing the linear or affine gap distance is polynomial and the time complexity for the concave gap distance is exponential.
Bibliographical noteFunding Information:
Ko and Han were supported by the Basic Science Research Program through NRF funded by MEST ( 2015R1D1A1A01060097 ), the Yonsei University Future-leading Research Initiative of 2015 and the International Cooperation Program managed by NRF of Korea ( 2014K2A1A2048512 ), and Salomaa was supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224 .
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics