---
res:
bibo_abstract:
- "Quantitative automata are nondeterministic finite automata with edge weights.
They value a\r\nrun by some function from the sequence of visited weights to the
reals, and value a word by its\r\nminimal/maximal run. They generalize boolean
automata, and have gained much attention in\r\nrecent years. Unfortunately, important
automaton classes, such as sum, discounted-sum, and\r\nlimit-average automata,
cannot be determinized. Yet, the quantitative setting provides the potential\r\nof
approximate determinization. We define approximate determinization with respect
to\r\na distance function, and investigate this potential.\r\nWe show that sum
automata cannot be determinized approximately with respect to any\r\ndistance
function. However, restricting to nonnegative weights allows for approximate determinization\r\nwith
respect to some distance functions.\r\nDiscounted-sum automata allow for approximate
determinization, as the influence of a word’s\r\nsuffix is decaying. However,
the naive approach, of unfolding the automaton computations up\r\nto a sufficient
level, is shown to be doubly exponential in the discount factor. We provide an\r\nalternative
construction that is singly exponential in the discount factor, in the precision,
and\r\nin the number of states. We prove matching lower bounds, showing exponential
dependency on\r\neach of these three parameters.\r\nAverage and limit-average
automata are shown to prohibit approximate determinization with\r\nrespect to
any distance function, and this is the case even for two weights, 0 and 1.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Udi
foaf_name: Boker, Udi
foaf_surname: Boker
foaf_workInfoHomepage: http://www.librecat.org/personId=31E297B6-F248-11E8-B48F-1D18A9856A87
- 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: 10.4230/LIPIcs.FSTTCS.2012.362
bibo_volume: 18
dct_date: 2012^xs_gYear
dct_language: eng
dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@
dct_title: Approximate determinization of quantitative automata@
...