Search Results

Documents authored by Richter, Linus

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.24
Languages of Words of Low Automatic Complexity Are Hard to Compute

Authors: Joey Chen, Bjørn Kjos-Hanssen, Ivan Koswara, Linus Richter, and Frank Stephan

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser’s distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet Σ of at least two elements, we consider the non-deterministic automatic complexity given by exactly - yet not necessarily uniquely - accepting automata: a word x ∈ Σ^* has exact non-deterministic automatic complexity k ∈ ℕ if there exists a non-deterministic automaton of k states which accepts x while rejecting every other word of the same length as x, and no automaton of fewer states has this property. Importantly, and in contrast to the classical notion, the witnessing automaton may have multiple paths of computation accepting x. We denote this measure of complexity by A_{Ne}, and study a class of languages of low A_{Ne}-complexity defined as L_q = {x ∈ Σ^* : A_{Ne}(x) < q|x|}, which is parameterised by rationals q ∈ (0,1/2) (generalising a class of sets first studied by Kjos-Hanssen). We show that for every q ∈ (0,1/2), this class is neither context-free nor recognisable by certain Boolean circuits. In the process, we answer an open question of Kjos-Hanssen quantifying the complexity of L_{1/3} in terms of Boolean circuits, and also prove the Shannon effect for A_{Ne}.
Cite as

Joey Chen, Bjørn Kjos-Hanssen, Ivan Koswara, Linus Richter, and Frank Stephan. Languages of Words of Low Automatic Complexity Are Hard to Compute. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chen_et_al:LIPIcs.FSTTCS.2025.24,
  author =	{Chen, Joey and Kjos-Hanssen, Bj{\o}rn and Koswara, Ivan and Richter, Linus and Stephan, Frank},
  title =	{{Languages of Words of Low Automatic Complexity Are Hard to Compute}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.24},
  URN =		{urn:nbn:de:0030-drops-251055},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.24},
  annote =	{Keywords: Automatic complexity, automata theory, formal languages, Boolean circuits, Shannon effect}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact