The Library
The big-O problem
Tools
Chistikov, Dmitry, Kiefer, Stefan, Murawski, Andrzej S. and Purser, David (2022) The big-O problem. Logical Methods in Computer Science, 18 (1). 40:1-40:50. doi:10.46298/lmcs-18(1:40)2022 ISSN 1860-5974.
|
PDF
WRAP-The-big-O-problem-Chistikov-2022.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (934Kb) | Preview |
Official URL: http://dx.doi.org/10.46298/lmcs-18(1:40)2022
Abstract
Given two weighted automata, we consider the problem of whether one is big-O of the other, i.e., if the weight of every finite word in the first is not greater than some constant multiple of the weight in the second. We show that the problem is undecidable, even for the instantiation of weighted automata as labelled Markov chains. Moreover, even when it is known that one weighted automaton is big-O of another, the problem of finding or approximating the associated constant is also undecidable. Our positive results show that the big-O problem is polynomial-time solvable for unambiguous automata, coNP-complete for unlabelled weighted automata (i.e., when the alphabet is a single character) and decidable, subject to Schanuel's conjecture, when the language is bounded (i.e., a subset of w∗1…w∗m for some finite words w1,…,wm) or when the automaton has finite ambiguity. On labelled Markov chains, the problem can be restated as a ratio total variation distance, which, instead of finding the maximum difference between the probabilities of any two events, finds the maximum ratio between the probabilities of any two events. The problem is related to ε-differential privacy, for which the optimal constant of the big-O notation is exactly exp(ε).
Item Type: | Journal Article | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | |||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | |||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Computer logic, Automatic theorem proving, Machine theory, Markov processes | |||||||||||||||||||||
Journal or Publication Title: | Logical Methods in Computer Science | |||||||||||||||||||||
Publisher: | International Federation for Computational Logic | |||||||||||||||||||||
ISSN: | 1860-5974 | |||||||||||||||||||||
Official Date: | 15 March 2022 | |||||||||||||||||||||
Dates: |
|
|||||||||||||||||||||
Volume: | 18 | |||||||||||||||||||||
Number: | 1 | |||||||||||||||||||||
Page Range: | 40:1-40:50 | |||||||||||||||||||||
DOI: | 10.46298/lmcs-18(1:40)2022 | |||||||||||||||||||||
Status: | Peer Reviewed | |||||||||||||||||||||
Publication Status: | Published | |||||||||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||||||||
Description: | Special Issue for CONCUR 2020 |
|||||||||||||||||||||
Date of first compliant deposit: | 28 March 2022 | |||||||||||||||||||||
Date of first compliant Open Access: | 8 April 2022 | |||||||||||||||||||||
RIOXX Funder/Project Grant: |
|
|||||||||||||||||||||
Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year