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EnglishWe consider the model of an iterated uniform finite-state transducer, which executes the same length-preserving transduction in iterative sweeps. The first sweep takes place on the input string, while any subsequent sweep works on the output of the previous one. We focus on unary languages. We show that any unary regular language can be accepted by a deterministic iterated uniform finite-state transducer with at most max{2⋅ϱ,p}+1max{2⋅ϱ,p}+1 states, where ϱϱ and p are the greatest primes in the factorization of the, respectively, pre-periodic and periodic part of the language. Such a state cost cannot be improved by using nondeterminism, and it turns out to be exponentially lower in the worst case than the state costs of equivalent classical models of finite-state automata. Next, we give a characterization of classes of unary languages accepted by non-constant sweep-bounded iterated uniform finite-state transducers in terms of time bounded one-way cellular automata. This characterization enables both to exhibit interesting families of unary non-regular languages accepted by iterated uniform finite-state transducers, and to prove the undecidability of several questions related to iterated uniform finite-state transducers accepting unary languages with an amount of sweeps that is at least logarithmic.
Iterated Uniform Finite-State Transducers on Unary Languages / M. Kutrib, A. Malcher, C. Mereghetti, B.S. Palano (LECTURE NOTES IN ARTIFICIAL INTELLIGENCE). - In: SOFSEM 2021: Theory and Practice of Computer Science / [a cura di] T. Bureš, R. Dondi, J. Gamper, G. Guerrini, T. Jurdziński, C. Pahl, F. Sikora, P.W.H. Wong. - [s.l] : Springer, 2021. - ISBN 9783030677305. - pp. 218-232 (( Intervento presentato al 47. convegno International Conference on Current Trends in Theory and Practice of Computer Science tenutosi a Bolzano nel 2021.
| Titolo: | Iterated Uniform Finite-State Transducers on Unary Languages |
| Autori: | PALANO, BEATRICE SANTA (Ultimo) (Corresponding) |
| Parole Chiave: | Iterated transducers; Unary languages; State complexity; Cellular automata; Undecidability results |
| Settore Scientifico Disciplinare: | Settore INF/01 - Informatica |
| Data di pubblicazione: | 2021 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/978-3-030-67731-2_16 |
| Tipologia: | Book Part (author) |
| Appare nelle tipologie: | 03 - Contributo in volume |
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