---
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_language: eng
dct_publisher: International Federation of Computational Logic@
dct_title: Expressiveness and closure properties for quantitative languages@
...