Approximate NFA Universality Motivated by Information Theory

• Type: Article in International Conference Proceedings Book
• Date: 2022

Authors

Konstantinidis, S (Author) Other; Mastnak, M (Author) Other; Nelma Moreira (Author) FCUP; Rogério Reis (Author) FCUP

Conference proceedings International

Title: DESCRIPTIONAL COMPLEXITY OF FORMAL SYSTEMS, DCFS 2022

Pages: 142-154

24th IFIP WG 1.02 International Conference on Descriptional Complexity of Formal Systems (DCFS)

Univ Debrecen, Debrecen, HUNGARY, AUG 29-31, 2022

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00X-4RQ

DOI: 10.1007/978-3-031-13257-5_11

Abstract (EN): In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is universal, and this is a hard problem (including the case of whether the NFA accepts all words of a fixed length). On the other hand, it is acceptable to know whether a code is `approximately' maximal, which then boils down to whether a given NFA is 'approximately' universal. Here we introduce the notion of a (1 - epsilon)universal automaton and present polynomial randomized approximation algorithms to test NFA universality and related hard automata problems, for certain natural probability distributions on the set of words. We also conclude that the randomization aspect is necessary, as approximate universality remains hard for any fixed polynomially computable epsilon.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13