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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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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