Abstract
We consider the complexity of equivalence and learning for multiplicity tree automata, i.e., weighted tree automata with weights in a field. We first show that the equivalence problem for multiplicity tree automata is logspace equivalent to polynomial identity testing. Secondly, we consider the problem of learning multiplicity tree automata in Angluin’s exact learning model. Here we give lower bounds on the number of queries, both for the case of an arbitrary and a fixed underlying field. We also present a learning algorithm in which trees are represented succinctly as DAGs. Assuming a Teacher that represents counterexamples as succinctly as possible, our algorithm uses exponentially fewer queries than the best previously known procedure, leaving only a polynomial gap with the above-mentioned lower bound. Moreover, fixing the alphabet rank, the query complexity of our algorithm matches the lower bound up to a constant factor.
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Marusic, I., Worrell, J. (2014). Complexity of Equivalence and Learning for Multiplicity Tree Automata. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_35
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DOI: https://doi.org/10.1007/978-3-662-44522-8_35
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