Abstract
Determinism plays an important role in grammatical inference. However, in practice, ambiguous grammars (and non determinism grammars in particular) are more used than determinism grammars. Computing the probability of parsing a given string or its most probable parse with stochastic regular grammars can be performed in linear time. However, the problem of finding the most probable string has yet not given any satisfactory answer. In this paper we prove that the problem is NP-hard and does not allow for a polynomial time approximation scheme. The result extends to stochastic regular syntax-directed translation schemes.
This work has been partially funded by the European Union and the Spanish CICYT, under grants IT-LTR-OS-30268 and TIC97-0745-C02, respectively.
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Casacuberta, F., de la Higuera, C. (2000). Computational Complexity of Problems on Probabilistic Grammars and Transducers. In: Oliveira, A.L. (eds) Grammatical Inference: Algorithms and Applications. ICGI 2000. Lecture Notes in Computer Science(), vol 1891. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45257-7_2
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DOI: https://doi.org/10.1007/978-3-540-45257-7_2
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