Quantitative languages Conference Paper


Author(s): Chatterjee, Krishnendu; Doyen, Laurent; Henzinger, Thomas A
Title: Quantitative languages
Title Series: LNCS
Affiliation
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 language inclusion 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.
Conference Title: CSL: Computer Science Logic
Volume: 5213
Conference Dates: September 16-19, 2008
Conference Location: Bertinoro, Italy
ISBN: 3-540-45458-6
Publisher: Springer  
Location: Berlin, Heidelberg
Date Published: 2008-09-10
Start Page: 385
End Page: 400
Sponsor: Research supported in part by the NSF grants CCR-0132780, CNS-0720884, and CCR-0225610, by the Swiss National Science Foundation, and by the European COMBEST project.
DOI: 10.1007/978-3-540-87531-4_28
Open access: no
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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