We study the determinisation and unambiguisation problems of weighted automata over the rational field: Given a weighted automaton, can we determine whether there exists an equivalent deterministic, respectively unambiguous, weighted automaton? Recent results by Bell and Smertnig show that the problem is decidable, however they do not provide any complexity bounds. We show that both problems are in PSPACE for polynomially-ambiguous weighted automata.

翻译：我们研究有理域上加权自动机的确定化与无歧义化问题：给定一个加权自动机，能否判定是否存在等价的确定性加权自动机（或等价的的无歧义加权自动机）？Bell和Smertnig的最新结果表明该问题可判定，但未给出任何复杂度界。我们证明，对于多项式模糊加权自动机，这两个问题均属于PSPACE。