Expressiveness and closure properties for quantitative languages Journal Article

Author(s): Chatterjee, Krishnendu; Doyen, Laurent; Henzinger, Thomas A
Article Title: Expressiveness and closure properties for quantitative languages
Affiliation IST Austria
Abstract: Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit-average, or discounted-sum of the transition weights. The value of a word w is the supremum of the values of the runs over w. We study expressiveness and closure questions about these quantitative languages. We first show that the set of words with value greater than a threshold can be omega-regular for deterministic limit-average and discounted-sum automata, while this set is always omega-regular when the threshold is isolated (i.e., some neighborhood around the threshold contains no word). In the latter case, we prove that the omega-regular language is robust against small perturbations of the transition weights. We next consider automata with transition weights 0 or 1 and show that they are as expressive as general weighted automata in the limit-average case, but not in the discounted-sum case. Third, for quantitative languages L-1 and L-2, we consider the operations max(L-1, L-2), min(L-1, L-2), and 1 - L-1, which generalize the boolean operations on languages, as well as the sum L-1 + L-2. We establish the closure properties of all classes of quantitative languages with respect to these four operations.
Keywords: quantitative verification; Weighted automata; Expressiveness and closure properties.
Journal Title: Logical Methods in Computer Science
Volume: 6
Issue 3:10
ISSN: 1860-5974
Publisher: International Federation of Computational Logic  
Date Published: 2010-08-30
Start Page: 1
End Page: 23
Copyright Statement: CC-BY-ND
DOI: 10.2168/LMCS-6(3:10)2010
Notes: This research was supported in part by the Swiss National Science Foundation under the Indo-Swiss Joint Research Programme, by the European Network of Excellence on Embedded Systems Design (ArtistDesign), by the European projects Combest, Quasimodo, and Gasics, by the PAI program Moves funded by the Belgian Federal Government, and by the CFV (Federated Center in Verification) funded by the F.R.S.- FNRS.
Open access: yes (OA journal)
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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