On Determinism and Unambiguity of Weighted Two-way Automata
  In this paper, we first study the conversion of weighted two-way automata to one-way automata. We show that this conversion preserves the unambiguity but does not preserve the determinism. Yet, we prove that the conversion of an unambiguous weighted one-way automaton into a two-way automaton leads to a deterministic two-way automaton. As a consequence, we prove that unambiguous weighted two-way automata are equivalent to deterministic weighted two-way automata in commutative semirings. 
Vincent Carnino (LIGM, Universit\'e Paris-Est), Sylvain Lombardy   (LaBRI, Insitut Polytechnique de Bordeaux)
cs.FL