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.Comment: In Proceedings AFL 2014, arXiv:1405.527
