Search Results

Documents authored by Scoones, Andrew

Document
DOI: 10.4230/LIPIcs.CSL.2025.18
Reachability for Multi-Priced Timed Automata with Positive and Negative Rates

Authors: Andrew Scoones, Mahsa Shirmohammadi, and James Worrell

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Multi-priced timed automata (MPTA) are timed automata with observer variables whose derivatives can change from one location to another. Observers are read-once variables: they do not affect the control flow of the automaton and their value is output only at the end of a run. Thus MPTA lie between timed and hybrid automata in expressiveness. Previous work considered observers with non-negative slope in every location. In this paper we treat observers that have both positive and negative rates. Our main result is an algorithm to decide a gap version of the reachability problem for this variant of MPTA. We translate the gap reachability problem into a gap satisfiability problem for mixed integer-real systems of nonlinear constraints. Our main technical contribution - a result of independent interest - is a procedure to solve such contraints via a combination of branch-and-bound and relaxation-and-rounding.
Cite as

Andrew Scoones, Mahsa Shirmohammadi, and James Worrell. Reachability for Multi-Priced Timed Automata with Positive and Negative Rates. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{scoones_et_al:LIPIcs.CSL.2025.18,
  author =	{Scoones, Andrew and Shirmohammadi, Mahsa and Worrell, James},
  title =	{{Reachability for Multi-Priced Timed Automata with Positive and Negative Rates}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.18},
  URN =		{urn:nbn:de:0030-drops-227758},
  doi =		{10.4230/LIPIcs.CSL.2025.18},
  annote =	{Keywords: Bilinear constraints, Existential theory of real closed fields, Diophantine approximation, Pareto curve}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.144
On Transcendence of Numbers Related to Sturmian and Arnoux-Rauzy Words

Authors: Pavol Kebis, Florian Luca, Joël Ouaknine, Andrew Scoones, and James Worrell

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider numbers of the form S_β(u): = ∑_{n=0}^∞ (u_n)/(βⁿ), where u = ⟨u_n⟩_{n=0}^∞ is an infinite word over a finite alphabet and β ∈ ℂ satisfies |β| > 1. Our main contribution is to present a combinatorial criterion on u, called echoing, that implies that S_β(u) is transcendental whenever β is algebraic. We show that every Sturmian word is echoing, as is the Tribonacci word, a leading example of an Arnoux-Rauzy word. We furthermore characterise ̅{ℚ}-linear independence of sets of the form {1, S_β(u₁),…,S_β(u_k)}, where u₁,…,u_k are Sturmian words having the same slope. Finally, we give an application of the above linear independence criterion to the theory of dynamical systems, showing that for a contracted rotation on the unit circle with algebraic slope, its limit set is either finite or consists exclusively of transcendental elements other than its endpoints 0 and 1. This confirms a conjecture of Bugeaud, Kim, Laurent, and Nogueira.
Cite as

Pavol Kebis, Florian Luca, Joël Ouaknine, Andrew Scoones, and James Worrell. On Transcendence of Numbers Related to Sturmian and Arnoux-Rauzy Words. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 144:1-144:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{kebis_et_al:LIPIcs.ICALP.2024.144,
  author =	{Kebis, Pavol and Luca, Florian and Ouaknine, Jo\"{e}l and Scoones, Andrew and Worrell, James},
  title =	{{On Transcendence of Numbers Related to Sturmian and Arnoux-Rauzy Words}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{144:1--144:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.144},
  URN =		{urn:nbn:de:0030-drops-202873},
  doi =		{10.4230/LIPIcs.ICALP.2024.144},
  annote =	{Keywords: Transcendence, Subspace Theorem, Fibonacci Word, Tribonacci Word}
}
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact