Abstract
Questions of economy of description are investigated in connection with single-valued finite transducers. The following results are shown. (1) Any single-valued real-time transducer M with n states can be effectively transformed into an equivalent unambiguous real-time transducer having at most 2n states. (2) Let M be a single-valued real-time transducer with n states and output alphabet δ which is equivalent to some deterministic real-time or subsequential transducer M′. Then, M can be effectively transformed into such an M′ having at most \(1 + 2^n \cdot \max \left\{ {2,\# \Delta } \right\}^{2n^3 l}\) states where l is a local structural parameter of M. (3) For any single-valued real-time transducer M it is decidable in deterministic polynomial time whether or not it is equivalent to some deterministic real-time transducer (to some subsequential transducer, respectively). The results (1)–(3) can be extended to the case that M is not real time. The upper bound in (1) is at most one state off the optimal upper bound. Any improvement of the upper bound in (2) is greater or equal than 2n.
A part of this research was done while the first author was supported by a Postdoctoral Fellowship of the Japan Society for the Promotion of Science
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References
K. Abrahamson, Succinct representation of regular sets using gotos and Boolean variables, J. Computer and System Sciences 34 (1987) 129–148.
J. Berstel, Transductions and Context-Free Languages, Teubner, Stuttgart, 1979.
C. Choffrut, Contribution à l'étude de quelques familles remarquables de fonctions rationnelles, thèse de doctorat d'état, Université Paris VII, 1978.
C. Choffrut and K. Culik II, Properties of finite and pushdown transducers, SIAM J. Computing 12 (1983) 300–315.
C. Choffrut and M.P. Schützenberger, Décomposition de fonctions rationnelles, Proc. 3rd STACS 1986, in: Lecture Notes in Computer Science 210, Springer, Berlin, Heidelberg, 1986, pp. 213–226.
S. Eilenberg, Automata, Languages, and Machines, Volume A, Academic Press, New York, NY, 1974.
E. Gurari, An Introduction to the Theory of Computation, Computer Science Press, Rockville, MD, 1989.
E. Gurari and O. Ibarra, A note on finite-valued and finitely ambiguous transducers, Mathematical Systems Theory 16 (1983) 61–66.
T. Harju, H.C.M. Kleijn, and M. Latteux, Compositional representation of rational functions, RAIRO Informatique théorique et Applications 26 (1992) 243–255.
T. Harju, H.C.M. Kleijn, and M. Latteux, Deterministic sequential functions, Acta Informatica 29 (1992) 545–554.
T. Head and A. Weber, Deciding code related properties by means of finite transducers, in: Sequences II, (R. Capocelli, A. De Santis, and U. Vaccaro, eds.), Springer, New York, NY, Berlin, Heidelberg, 1993, pp. 260–272.
J. Hopcroft and J. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, MA, 1979.
C. Kintala, K.-Y. Pun, and D. Wotschke, Concise representations of regular languages by degree and probabilistic finite automata, Mathematical Systems Theory 26 (1993) 379–395.
C. Kintala and D. Wotschke, Amounts of nondeterminism in finite automata, Acta Informatica 13 (1980) 199–204.
H. Leung, personal communication, 1991.
H. Leung, Separating exponentially ambiguous NFA from polynomially ambiguous NFA, Proc. 4th ISAAC 1993, in: Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, to appear.
R. Lyndon and P. Schupp, Combinatorial Group Theory, Springer, Berlin, Heidelberg, New York, NY, 1977.
A. Meyer and M. Fischer, Economy of description by automata, grammars, and formal systems, Proc. 12th SWAT 1971, pp. 188–191.
F.R. Moore, On the bounds for state-set size in the proofs of equivalence between deterministic, nondeterministic, and two-way finite automata, IEEE Transactions on Computers 20 (1971) 1211–1214.
J.-E. Pin, On reversible automata, Proc. 1st LATIN 1992, in: Lecture Notes in Computer Science 583, Springer, Berlin, Heidelberg, 1992, pp. 401–416.
B. Ravikumar and O. Ibarra, Relating the type of ambiguity of finite automata to the succinctness of their representation, SIAM J. Computing 18 (1989) 1263–1282.
C. Reutenauer, Subsequential functions: characterizations, minimization, examples, Proc. 6th IMYCS 1990, in: Lecture Notes in Computer Science 464, Springer, Berlin, Heidelberg, 1991, pp. 62–79.
E.M. Schmidt, Succinctness of descriptions of context-free, regular, and finite languages, Ph.D. thesis, Cornell University, 1978.
M.P. Schützenberger, Sur les relations rationnelles entre monoÏdes libres, Theoretical Computer Science 3 (1976) 243–259.
H. Seidl, When is a functional tree transduction deterministic? Proc. 4th TAPSOFT 1993, in: Lecture Notes in Computer Science 668, Springer, Berlin, Heidelberg, 1993, pp. 251–265.
R. Stearns and H. Hunt III, On the equivalence and containment problems for unambiguous regular expressions, regular grammars and finite automata, SIAM J. Computing 14 (1985) 598–611.
V.A. Uspensky, Complexity and entropy: an introduction to the theory of Kolmogorov complexity, in: Kolmogorov Complexity and Computational Complexity, (O. Watanabe, ed.), Springer, Berlin, Heidelberg, 1992, pp. 85–102.
A. Weber, On the valuedness of finite transducers, Acta Informatica 27 (1990) 749–780.
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Weber, A., Klemm, R. (1994). Economy of description for single-valued transducers. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_175
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