Abstract
Given a context-free grammar (CFG) and a finite-state automaton (FA), we tackle the problem of computing the most similar pair of strings from two languages. We in particular consider three different gap cost models, linear, affine and concave models, that are crucial for finding a proper alignment between two bio sequences. We design efficient algorithms for computing 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.
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References
Aho, A., Peterson, T.: A minimum distance error-correcting parser for context-free languages. SIAM Journal on Computing 1(4), 305–312 (1972)
Bellman, R.: On a routing problem. Quarterly of Applied Mathematics 16, 87–90 (1958)
Choffrut, C., Pighizzini, G.: Distances between languages and reflexivity of relations. Theoretical Computer Science 286(1), 117–138 (2002)
Cocke, J.: Programming languages and their compilers: Preliminary notes. Courant Institute of Mathematical Sciences. New York University (1969)
Dijkstra, E.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)
Earley, J.: An efficient context-free parsing algorithm. Communications of the ACM 13(2), 94–102 (1970)
Floyd, R.W.: Algorithm 97: Shortest path. Communications of the ACM 5(6), 345–348 (1962)
Younger, D.H.: Recognition and parsing of context-free languages in time n 3. Information and Control 10(2), 189–208 (1967)
Han, Y.-S., Ko, S.-K., Salomaa, K.: Computing the edit-distance between a regular language and a context-free language. In: Yen, H.-C., Ibarra, O.H. (eds.) DLT 2012. LNCS, vol. 7410, pp. 85–96. Springer, Heidelberg (2012)
Hopcroft, J., Ullman, J.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Addison-Wesley, Reading (1979)
Kari, L., Konstantinidis, S.: Descriptional complexity of error/edit systems. Journal of Automata, Languages and Combinatorics 9, 293–309 (2004)
Kasami, T.: An efficient recognition and syntax-analysis algorithm for context-free languages. Technical report, Air Force Cambridge Research Lab, Bedford, MA (1965)
Knight, J.R., Myers, E.W.: Approximate regular expression pattern matching with concave gap penalties. Algorithmica 14, 67–78 (1995)
Konstantinidis, S.: Computing the edit distance of a regular language. Information and Computation 205, 1307–1316 (2007)
Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Soviet Physics Doklady 10(8), 707–710 (1966)
Lyon, G.: Syntax-directed least-errors analysis for context-free languages: a practical approach. Communications of the ACM 17(1), 3–14 (1974)
Miller, W., Myers, E.W.: Sequence comparison with concave weighting functions. Bulletin of Mathematical Biology 50(2), 97–120 (1988)
Mohri, M.: Edit-distance of weighted automata: General definitions and algorithms. International Journal of Foundations of Computer Science 14(6), 957–982 (2003)
Myers, G.: Approximately matching context-free languages. Information Processing Letters 54, 85–92 (1995)
Needleman, S.B., Wunsch, C.D.: A general method applicable to the search for similarities in the amino acid sequence of two proteins. Journal of Molecular Biology 48(3), 443–453 (1970)
Sankoff, D., Kruskal, J.B.: Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison. Addison-Wesley (1983)
Waterman, M.S.: Efficient sequence alignment algorithms. Journal of Theoretical Biology 108, 333–337 (1984)
Wood, D.: Theory of Computation. Harper & Row (1987)
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Han, YS., Ko, SK., Salomaa, K. (2013). Approximate Matching between a Context-Free Grammar and a Finite-State Automaton. In: Konstantinidis, S. (eds) Implementation and Application of Automata. CIAA 2013. Lecture Notes in Computer Science, vol 7982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39274-0_14
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DOI: https://doi.org/10.1007/978-3-642-39274-0_14
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