---
res:
  bibo_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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Krishnendu
      foaf_name: Chatterjee, Krishnendu
      foaf_surname: Chatterjee
      foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-4561-241X
  - foaf_Person:
      foaf_givenName: Laurent
      foaf_name: Doyen, Laurent
      foaf_surname: Doyen
  - foaf_Person:
      foaf_givenName: Thomas A
      foaf_name: Henzinger, Thomas A
      foaf_surname: Henzinger
      foaf_workInfoHomepage: http://www.librecat.org/personId=40876CD8-F248-11E8-B48F-1D18A9856A87
    orcid: 0000−0002−2985−7724
  bibo_doi: 10.2168/LMCS-6(3:10)2010
  bibo_issue: '3'
  bibo_volume: 6
  dct_date: 2010^xs_gYear
  dct_identifier:
  - UT:000282653500010
  dct_language: eng
  dct_publisher: International Federation for Computational Logic@
  dct_title: Expressiveness and closure properties for quantitative languages@
...