湿重对称自动自动自动交换的Nivat理论论 (A Nivat Theorem for Weighted Alternating Automata over Commutative Semirings)

In this paper, we give a Nivat-like characterization for weighted alternating automata over commutative semirings (WAFA). To this purpose we prove that weighted alternating can be characterized as the concatenation of weighted finite tree automata (WFTA) and a specific class of tree homomorphism. We show that the class of series recognized by weighted alternating automata is closed under inverses of homomorphisms, but not under homomorphisms. We give a logical characterization of weighted alternating automata, which uses weighted MSO logic for trees. Finally we investigate the strong connection between weighted alternating automata and polynomial automata. Using the corresponding result for polynomial automata, we are able to prove that the ZERONESS problem for weighted alternating automata with the rational numbers as weights is decidable.

翻译：在本文中,我们给出了对交替加权自动数据对交替流动半径(WAFA)的类似Nivat特征特征。为此,我们证明加权交替可被定性为加权定数树自动成形(WFTA)和特定树同质性类别。我们证明,加权交替自动成形(WFTA)所认可的系列类别在反同质制下被封闭,而不是在同质制下。我们给出了加权交替自动数据逻辑特征的逻辑特征,该数据对树木使用加权 MSO 逻辑。最后,我们调查了加权交替自动成形和多元自动成形之间的紧密联系。我们利用多元自动成形的相应结果,能够证明加权交替自动成形与合理数字的加权交替自动成份的ZERONESS问题是可变的。