Quantitative languages

K. Chatterjee, L. Doyen, T.A. Henzinger, ACM Transactions on Computational Logic (TOCL) 11 (2010) 23.

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Journal Article | Published | English
Abstract
Quantitative generalizations of classical languages, which assign to each word a real number instead of a Boolean value, have applications in modeling resource-constrained computation. We use weighted automata (finite automata with transition weights) to define several natural classes of quantitative languages over finite and infinite words; in particular, the real value of an infinite run is computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We define the classical decision problems of automata theory (emptiness, universality, language inclusion, and language equivalence) in the quantitative setting and study their computational complexity. As the decidability of the language-inclusion problem remains open for some classes of weighted automata, we introduce a notion of quantitative simulation that is decidable and implies language inclusion. We also give a complete characterization of the expressive power of the various classes of weighted automata. In particular, we show that most classes of weighted automata cannot be determinized.
Publishing Year
Date Published
2010-07-01
Journal Title
ACM Transactions on Computational Logic (TOCL)
Volume
11
Issue
4
Article Number
23
IST-REx-ID

Cite this

Chatterjee K, Doyen L, Henzinger TA. Quantitative languages. ACM Transactions on Computational Logic (TOCL). 2010;11(4):23. doi:10.1145/1805950.1805953
Chatterjee, K., Doyen, L., & Henzinger, T. A. (2010). Quantitative languages. ACM Transactions on Computational Logic (TOCL), 11(4), 23. https://doi.org/10.1145/1805950.1805953
Chatterjee, Krishnendu, Laurent Doyen, and Thomas A Henzinger. “Quantitative Languages.” ACM Transactions on Computational Logic (TOCL) 11, no. 4 (2010): 23. https://doi.org/10.1145/1805950.1805953.
K. Chatterjee, L. Doyen, and T. A. Henzinger, “Quantitative languages,” ACM Transactions on Computational Logic (TOCL), vol. 11, no. 4, p. 23, 2010.
Chatterjee K, Doyen L, Henzinger TA. 2010. Quantitative languages. ACM Transactions on Computational Logic (TOCL). 11(4), 23.
Chatterjee, Krishnendu, et al. “Quantitative Languages.” ACM Transactions on Computational Logic (TOCL), vol. 11, no. 4, ACM, 2010, p. 23, doi:10.1145/1805950.1805953.
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