---
res:
bibo_abstract:
- 'A discounted-sum automaton (NDA) is a nondeterministic finite automaton with
edge weights, which values a run by the discounted sum of visited edge weights.
More precisely, the weight in the i-th position of the run is divided by lambda^i,
where the discount factor lambda is a fixed rational number greater than 1. Discounted
summation is a common and useful measuring scheme, especially for infinite sequences,
which reflects the assumption that earlier weights are more important than later
weights. Determinizing automata is often essential, for example, in formal verification,
where there are polynomial algorithms for comparing two deterministic NDAs, while
the equivalence problem for NDAs is not known to be decidable. Unfortunately,
however, discounted-sum automata are, in general, not determinizable: it is currently
known that for every rational discount factor 1 < lambda < 2, there is an
NDA with lambda (denoted lambda-NDA) that cannot be determinized. We provide positive
news, showing that every NDA with an integral factor is determinizable. We also
complete the picture by proving that the integers characterize exactly the discount
factors that guarantee determinizability: we show that for every non-integral
rational factor lambda, there is a nondeterminizable lambda-NDA. Finally, we prove
that the class of NDAs with integral discount factors enjoys closure under the
algebraic operations min, max, addition, and subtraction, which is not the case
for general NDAs nor for deterministic NDAs. This shows that for integral discount
factors, the class of NDAs forms an attractive specification formalism in quantitative
formal verification. All our results hold equally for automata over finite words
and for automata over infinite words. @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.CSL.2011.82
bibo_volume: 12
dct_date: 2011^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: Determinizing discounted-sum automata@
...