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.
Accepté le :
DOI : 10.1051/ita/2016026
Mots clés : Two-way automata, weighted automata, formal power series
@article{ITA_2016__50_4_331_0, author = {Lombardy, Sylvain}, title = {Two-way representations and weighted automata}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {331--350}, publisher = {EDP-Sciences}, volume = {50}, number = {4}, year = {2016}, doi = {10.1051/ita/2016026}, mrnumber = {3614549}, zbl = {1362.68150}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita/2016026/} }
TY - JOUR AU - Lombardy, Sylvain TI - Two-way representations and weighted automata JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2016 SP - 331 EP - 350 VL - 50 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2016026/ DO - 10.1051/ita/2016026 LA - en ID - ITA_2016__50_4_331_0 ER -
%0 Journal Article %A Lombardy, Sylvain %T Two-way representations and weighted automata %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2016 %P 331-350 %V 50 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2016026/ %R 10.1051/ita/2016026 %G en %F ITA_2016__50_4_331_0
Lombardy, Sylvain. Two-way representations and weighted automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 4, pp. 331-350. doi : 10.1051/ita/2016026. http://archive.numdam.org/articles/10.1051/ita/2016026/
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