Abstract
An extension to finite state transducers is presented, in which atomic symbols are replaced by arbitrary predicates over symbols. The extension is motivated by applications in natural language processing (but may be more widely applicable) as well as by the observation that transducers with predicates generally have fewer states and fewer transitions. Although the extension is fairly trivial for finite state acceptors, the introduction of predicates is more interesting for transducers. It is shown how various operations on transducers (e.g., composition) can be implemented, as well as how the transducer determinization algorithm can be generalized for predicate-augmented finite state transducers.
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REFERENCES
Aho, A. V., J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, MA, 1974.
Aho, A. V., R. Sethi, and J. D. Ullman. Compilers. Principles, Techniques and Tools. Addison Wesley, Reading, MA, 1986.
Bird, S. and T. M. Ellison. One-Level Phonology: Autosegmental Representations and Rules as Finite Automata. Computational Linguistics, 20(1), 55–90, 1994.
Carpenter, B. The Logic of Typed Feature Structures. Cambridge University Press, New York, 1992.
Daciuk, J. Incremental Construction of Finite-state Automata and Transducers, and their Use in the Natural Language Processing. Ph.D. thesis, Technical University of Gdańsk, 1998.
Daciuk, J. Experiments with Automata Compression. In: M. Daley, M. G. Eramian, and S. Yu (eds.): Proceedings of the Conference on Implementation and Application of Automata CIAA'2000. London, Ontario, Canada, pp. 113–119, University of Western Ontario, 2000.
Dassow, J., G. Paun, and A. Salomaa. Grammars with Controlled Derivations. In: G. Rozenberg and A. Salomaa (eds.): Handbook of Formal Languages Vol.2 Linear Modeling: Background and Application. Springer, Berlin, pp. 101–154, 1997.
Eisner, J. Efficient Generation in Primitive Optimality Theory. In: Proceedings of the 35th Annual Meeting of the Association for Computational Linguistics and 8th Conference of the European Chapter of the Association for Computational Linguistics pp. 313–320, 1997.
Gerdemann, D. and G. van Noord. Transducers from Rewrite Rules with Backreferences. In: Pro-ceedings of the Ninth Conference of the European Chapter of the Association for Computational Linguistics. Bergen, Norway, pp. 126–133, 1999.
Gildea, D. and D. Jurafsky: Learning Bias and Phonological-Rule Induction. Computational Linguistics, 22(4): 497–530, 1996.
Hopcroft, J.E. An log n algorithm for minimizing the states in a finite automaton. In: Z. Kohavi (ed.): The Theory of Machines and Computations. Academic Press, New York, pp. 189–196, 1971.
Hopcroft, J. E. and J. D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison Wesley, Reading, MA, 1979.
Johnson, J. H. and D. Wood. Instruction Computation in Subset Construction. In: D. Raymond, D. Wood, and S. Yu (eds.): Automata Implementation. Springer, Berlin, pp. 64–71. Lecture Notes in Computer Science 1260, 1997.
Karttunen, L. Finite-state Constraints. In: Proceedings of the International Conference on Current Issues in Computational Linguistics. Universiti Sains Malaysia, Penang, pp. 23–40, 1991.
Karttunen, L. The Replace Operator. In: 33th Annual Meeting of the Association for Computational Linguistics. M.I.T., Cambridge Press, MA, pp. 16–23, 1995.
Karttunen, L. Directed Replacement. In: Proceedings of the 34th Annual Meeting of the Association for Computational Linguistics. Santa Cruz, pp. 108–115, 1996.
Karttunen, L., J.-P. Chanod, G. Grefenstette, and A. Schiller. Regular Expressions for Language Engineering. Natural Language Engineering, 2(4), 305–238, 1996. http://www.rxrc.xerox.com/research/mltt/fst/articles/jnle-97/rele.html
Kempe, A. Factorization of Ambiguous Finite-State Transducers. In: CIAA 2000. Fifth International Conference on Implementation and Application of Automata. Preproceedings. London, Ontario, Canada, pp. 157–164, 2000.
Kempe, A. and L. Karttunen. Parallel Replacement in the Finite-State Calculus. In: Proceedings of the 16th International Conference on Computational Linguistics (COLING). Copenhagen, Denmark, pp. 622–627, 1996.
Kiraz, G. A. Compressed Storage of Sparse Finite-State Transducers. In: O. Boldt, H. Jürgensen, and L. Robbins (eds.): Workshop on Implementing Automata WIA99-Pre-Proceedings. Potsdam, 1999.
Klarlund, N. Mona & Fido: The Logic-Automaton Connection in Practice. In: Computer Science Logic, CSL 97. Springer, Berlin. Lecture Notes in Computer Science 1414, 1998.
Knuth, D. E. The Art of Computer Programming, Volume 3, Sorting and Searching. Addison Wesley, Reading, MA, second edition, 1998.
Kowaltowski, T., C. L. Lucchesi, and J. Stolfi. Minimization of Binary Automata. In: Proceedings of the First South American String Processing Workshop. Belo Horizonte, Brazil
Mohri, M. ‘Compact Representations by Finite-State Transducers’. In: Proceedings of the 32th Annual Meeting of the Association for Computational Linguistics. New Mexico State University, pp. 204–209, 1994.
Mohri, M. On Some Applications of Finite-State Automata Theory to Natural Language Processing. Natural Language Engineering, 2, 61–80, 1996. Originally appeared in 1994 as Technical Report, institut Gaspard Monge, Paris.
Mohri, M. Minimization Algorithms for Sequential Transducers. Theoretical Computer Science, 234, 177–201, 2000.
Oncina, J., P. García and E. Vidal. Learning Subsequential Transducers for Pattern Recognition Inter-pretation Tasks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15, 448–458, 1993.
Perrin, D. Finite Automata. In: J. van Leeuwen (ed.): Handbook of Theoretical Computer Science. Volume B: Formal Models and Semantics. Elsevier and the MIT Press, Amsterdam and Cambridge, MA, pp. 1–57, 1990.
Reutenauer, C. Subsequential Functions: Characterizations, Minimization, Examples. In: Proceedings of the International Meeting of Young Computer Scientists. Springer, Berlin. Lecture Notes in Computer Science, 1993.
Roche, E. and Y. Schabes, Deterministic Part-of-speech Tagging with Finitestate Transducers. Computational Linguistics, 21(2), 227–253, 1995.
Roche, E. and Y. Schabes. Introduction. In: E. Roche and Y. Schabes (eds.): Finite-State Language Processing. MIT Press, Cambridge, MA, 1997.
Sterling, L. and E. Shapiro. The Art of Prolog. MIT Press, Cambridge MA, Second Edition, 1994.
van Noord, G. and D. Gerdemann. ‘An Extendible Regular Expression Compiler for Finite-state Approaches in Natural Language Processing’. In: O. Boldt, H. Juergensen, and L. Robbins (eds.): Workshop on Implementing Automata, WIA99-Pre-Proceedings Potsdam, 1999.
Walther, M. ‘One-Level Prosodic Morphology’. Technical Report 1, Institüt für Germanistische Sprachwissenschaft, Philipps-Universität Marbug, 1999.
Walther, M. ‘Finite-State Reduplication in One-Level Prosodic Morphology’. In: Proceedings of the First Conference of the North American Chapter of the Association for Computational Linguistics. Seattle, pp. 296–302, 2000.
Watson, B. W. Implementing and Using Finite Automata Toolkits. In: A. Kornai (ed.): Extended Finite State Models of Language. Cambridge University Press, Cambridge, pp. 19–36, 1999a.
Watson, B. W. The OpenFIRE Initiative. In: J. Aoe (ed.): Proceedings of the International Conference on Computer Processing of Oriental Languages. Tokushima, Japan, pp. 421–424, 1999b.
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van Noord, G., Gerdemann, D. Finite State Transducers with Predicates and Identities. Grammars 4, 263–286 (2001). https://doi.org/10.1023/A:1012291501330
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DOI: https://doi.org/10.1023/A:1012291501330