Abstract
Nested words have been introduced by Alur and Madhusudan as a model for e.g. recursive programs or XML documents and have received much recent interest. In this paper, we investigate a quantitative automaton model and a quantitative logic for nested words. The behavior resp. the semantics map nested words to weights taken from a strong bimonoid. Strong bimonoids can be viewed as semirings without requiring the distributivity assumption which was essential in the classical theory of formal power series; strong bimonoids include e.g. all bounded lattices and many other structures from multi-valued logics. Our main results show that weighted nested word automata and suitable weighted MSO logics are expressively equivalent. This extends the classical Büchi-Elgot result from words to a weighted setting for nested words.
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This work has been supported by DFG-NRCT.
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Droste, M., Pibaljommee, B. (2012). Weighted Nested Word Automata and Logics over Strong Bimonoids. In: Moreira, N., Reis, R. (eds) Implementation and Application of Automata. CIAA 2012. Lecture Notes in Computer Science, vol 7381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31606-7_12
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