Quantitative languages Journal Article


Author(s): Chatterjee, Krishnendu; Doyen, Laurent; Henzinger, Thomas A
Article Title: Quantitative languages
Affiliation IST Austria
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.
Journal Title: ACM Transactions on Computational Logic (TOCL)
Volume: 11
Issue 4:23
ISSN: 1557-945X
Publisher: ACM  
Date Published: 2010-07-01
Start Page: 1
End Page: 38
URL:
DOI: 10.1145/1805950.1805953
Notes: We thank anonymous reviewers for helpful comments.
Open access: yes (repository)
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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