Paper Info
Title
Aperiodic Weighted Automata and Weighted First-Order Logic.
Abstract
By fundamental results of Sch\"utzenberger, McNaughton and Papert from the 1970s, the classes of first-order definable and aperiodic languages coincide. Here, we extend this equivalence to a quantitative setting. For this, weighted automata form a general and widely studied model. We define a suitable notion of a weighted first-order logic. Then we show that this weighted first-order logic and aperiodic polynomially ambiguous weighted automata have the same expressive power. Moreover, we obtain such equivalence results for suitable weighted sublogics and finitely ambiguous or unambiguous aperiodic weighted automata. Our results hold for general weight structures, including all semirings, average computations of costs, bounded lattices, and others.
Year
DOI
Venue
2019
10.4230/LIPIcs.MFCS.2019.76
MFCS
DocType
Volume
Issue
Journal
abs/1902.08149
138
Citations 
PageRank 
References 
0
0.34
16
Authors
2
Name
Order
Citations
PageRank
Manfred Droste181672.86
Paul Gastin2116575.66