Two-way representations and weighted automata
Lombardy, Sylvain1
1 Institut Polytechnique de Bordeaux, LaBRI, UMR 5800, France.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, 7th Non-Classical Models of Automata and Applications (NCMA-2015) , Tome 50 (2016) no. 4, pp. 331-350.

We study the series realized by weighted two-way automata, that are strictly more powerful than weighted one-way automata. To this end, we consider the Hadamard product and the Hadamard iteration of formal power series. We introduce two-way representations and show that the series they realize are the solutions of fixed-point equations. In rationally additive semirings, we prove that two-way automata are equivalent to two-way representations, and, for some specific classes of two-way automata, rotating and sweeping automata, we give a characterization of the series that can be realized.

Reçu le :
Accepté le :
DOI : 10.1051/ita/2016026
Classification : 68Q45, 68Q70
Mots-clés : Two-way automata, weighted automata, formal power series
Lombardy, Sylvain 1

1 Institut Polytechnique de Bordeaux, LaBRI, UMR 5800, France. 
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Lombardy, Sylvain. Two-way representations and weighted automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, 7th Non-Classical Models of Automata and Applications (NCMA-2015) , Tome 50 (2016) no. 4, pp. 331-350. doi : 10.1051/ita/2016026. http://www.numdam.org/articles/10.1051/ita/2016026/

M. Anselmo, Two-way automata with multiplicity. In ICALP’90. Vol. 443 of Lect. Notes Comput. Sci. Springer (1990) 88–102. | MR | Zbl

M. Anselmo and A. Bertoni, Two-way probabilistic automata and rational power series. In vol. 923 Proc. of IV Conv. It. Inform. Teor. World Scientific (1992). | MR

J.-C. Birget, Concatenation of inputs in a two-way automaton. Theoret. Comput. Sci. 63 (1989) 141–156. | DOI | MR | Zbl

J.-C. Birget, Two-way automaton computations. RAIRO Inform. Théor. App. 24 (1990) 47–66. | DOI | Numdam | MR | Zbl

S. L. Bloom and Z. Ésik, Iteration Theories: The equational logic of iterative processes. Monogr. Theoret. Comput. Sci. EATCS Ser., Springer Verlag (1993). | MR

V. Carnino and S. Lombardy, On Determinism and Unambiguity of Weighted Two-way Automata. In AFL’14, Vol. 151 of EPTCS (2014) 188–200. | MR

V. Carnino and S. Lombardy, Tropical Two-Way Automata. In TCS’14, Vol. 8705 of Lect. Notes Comput. Sci., Springer (2014) 195–206. | MR

Ch. Choffrut and B. Guillon, An algebraic characterization of unary two-way transducers. In MFCS’14, Vol. 8634 of Lect. Notes Comput. Sci., Springer (2014) 196–207. | MR

J.H. Conway, Regular Algebra and Finite Machines. Chapman and Hall, London (1971). | MR | Zbl

Z. Ésik and W. Kuich, Rationally additive semirings. J. UCS 8 (2002) 173–183. | MR | Zbl

M. Fliess, Matrices de hankel. J. Math Pures Appl. 53 (1974) 197–222. | MR | Zbl

P. Gastin and B. Monmege, Adding pebbles to weighted automata: Easy specification & efficient evaluation. Theoret. Comp. Sci. 534 (2014) 24–44. | DOI | MR | Zbl

B. Guillon, Sweeping weakens two-way transducers even with a unary output alphabet. In NCMA’15, Vol. 318 of books@ocg.at, Austrian Comput. Soc. (2015) 91–108.

R. Mcnaughton and H. Yamada, Regular expressions and state graphs for automata. IRE Trans. Electronic Computers 9 (1960) 39–47. | DOI | Zbl

J.-Pierre Pécuchet, Automates boustrophedon, semi-groupe de birget et monoide inversif libre. RAIRO Inform. Théor. App. 19 (1985) 71–100. | DOI | Numdam | MR | Zbl

G. Pighizzini, Two-way finite automata: Old and recent results. Fundam. Inform. 126 (2013) 225–246. | DOI | MR | Zbl

M.O. Rabin and D. Scott, Finite automata and their decision problems. IBM J. Res. Dev. 3 (1959) 114–125. | DOI | MR | Zbl

Ch. Reutenauer, Sur les éléments inversibles de l’algèbre de Hadamard des séries rationnelles. Bull. Soc. Math. France 110 (1982) 225–232. | DOI | Numdam | MR | Zbl

J. Sakarovitch, Elements of Automata Theory. Cambridge University Press (2009). | MR | Zbl

M.-P. Schützenberger, On the definition of a family of automata. Inform. and Control 4 (1961) 245–270. | DOI | MR | Zbl

J.C. Shepherdson, The reduction of two-way automata to one-way automata. IBM J. Res. Dev. 3 (1959) 198–200. | DOI | MR | Zbl

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