RAIRO-Theor. Inf. Appl.
Volume 50, Number 4, October-December 20167th Non-Classical Models of Automata and Applications (NCMA-2015)
|Page(s)||331 - 350|
|Published online||09 January 2017|
Two-way representations and weighted automata
Institut Polytechnique de Bordeaux, LaBRI, UMR 5800, France.
Received: 25 January 2016
Accepted: 7 November 2016
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.
Mathematics Subject Classification: 68Q45 / 68Q70
Key words: Two-way automata / weighted automata / formal power series
© EDP Sciences 2017
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