---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22406'
abstract:
- lang: eng
  text: "It is known that for a uniform morphic sequence \U0001D496 =⟨\U0001D462\U0001D45B⟩∞\r\n\U0001D45B=0
    and an algebraic number \U0001D6FD such that |\U0001D6FD| >1, the number [[\U0001D496]]\U0001D6FD
    :=∑∞\r\n\U0001D45B=0(\U0001D462\U0001D45B/\U0001D6FD\U0001D45B) either lies in
    ℚ⁡(\U0001D6FD) or is transcendental. In this paper, we show a similar rational–transcendental
    dichotomy for sequences defined by irreducible Pisot morphisms on binary alphabets.
    Subject to the Pisot conjecture (an irreducible Pisot morphism has pure discrete
    spectrum), we generalise the latter result to arbitrary finite alphabets. In certain
    cases, we are able to show transcendence of [[\U0001D496]]\U0001D6FD outright.
    In particular, for \U0001D458 ≥2, if \U0001D496 is the k-Bonacci word, then [[\U0001D496]]\U0001D6FD
    is transcendental."
acknowledgement: "We thank the anonymous referee for identifying an error in an earlier\r\nversion
  of the paper. We gratefully acknowledge support from UKRI Frontier Research\r\nGrant
  EP/X033813/1, ERC grant DynAMiCS (101167561) and DFG grant 389792660 as\r\npart
  of TRR 248. J.O. is also affiliated with Keble College, Oxford as an Emmy Network\r\nfellow."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Pavol
  full_name: Kebis, Pavol
  id: 2e0132b3-4e98-11ef-b275-cf7281c2802a
  last_name: Kebis
- first_name: FLORIAN
  full_name: LUCA, FLORIAN
  last_name: LUCA
- first_name: JOEL
  full_name: OUAKNINE, JOEL
  last_name: OUAKNINE
- first_name: ANDREW
  full_name: SCOONES, ANDREW
  last_name: SCOONES
- first_name: JAMES
  full_name: WORRELL, JAMES
  last_name: WORRELL
citation:
  ama: Kebis P, LUCA F, OUAKNINE J, SCOONES A, WORRELL J. Transcendence for Pisot
    morphic words over an algebraic base. <i>Ergodic Theory and Dynamical Systems</i>.
    2026:1-22. doi:<a href="https://doi.org/10.1017/etds.2026.10324">10.1017/etds.2026.10324</a>
  apa: Kebis, P., LUCA, F., OUAKNINE, J., SCOONES, A., &#38; WORRELL, J. (2026). Transcendence
    for Pisot morphic words over an algebraic base. <i>Ergodic Theory and Dynamical
    Systems</i>. Cambridge University Press. <a href="https://doi.org/10.1017/etds.2026.10324">https://doi.org/10.1017/etds.2026.10324</a>
  chicago: Kebis, Pavol, FLORIAN LUCA, JOEL OUAKNINE, ANDREW SCOONES, and JAMES WORRELL.
    “Transcendence for Pisot Morphic Words over an Algebraic Base.” <i>Ergodic Theory
    and Dynamical Systems</i>. Cambridge University Press, 2026. <a href="https://doi.org/10.1017/etds.2026.10324">https://doi.org/10.1017/etds.2026.10324</a>.
  ieee: P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, and J. WORRELL, “Transcendence
    for Pisot morphic words over an algebraic base,” <i>Ergodic Theory and Dynamical
    Systems</i>. Cambridge University Press, pp. 1–22, 2026.
  ista: Kebis P, LUCA F, OUAKNINE J, SCOONES A, WORRELL J. 2026. Transcendence for
    Pisot morphic words over an algebraic base. Ergodic Theory and Dynamical Systems.,
    1–22.
  mla: Kebis, Pavol, et al. “Transcendence for Pisot Morphic Words over an Algebraic
    Base.” <i>Ergodic Theory and Dynamical Systems</i>, Cambridge University Press,
    2026, pp. 1–22, doi:<a href="https://doi.org/10.1017/etds.2026.10324">10.1017/etds.2026.10324</a>.
  short: P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, J. WORRELL, Ergodic Theory and
    Dynamical Systems (2026) 1–22.
das_tickbox: '0'
date_created: 2026-07-27T05:53:25Z
date_published: 2026-07-10T00:00:00Z
date_updated: 2026-08-03T06:17:50Z
day: '10'
ddc:
- '000'
department:
- _id: ToHe
- _id: GradSch
doi: 10.1017/etds.2026.10324
external_id:
  arxiv:
  - '2405.05279'
fulldoi: https://doi.org/10.1017/etds.2026.10324
has_accepted_license: '1'
keyword:
- balanced-pair algorithm
- Cobham’s conjecture
- k-Bonacci words
- Pisot conjecture
- subspace theorem
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1017/etds.2026.10324
mathsc:
- 11J81
- 37B10
- 11J87
month: '07'
oa: 1
oa_version: Published Version
page: 1-22
publication: Ergodic Theory and Dynamical Systems
publication_identifier:
  eissn:
  - 1469-4417
  issn:
  - 0143-3857
publication_status: epub_ahead
publisher: Cambridge University Press
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Transcendence for Pisot morphic words over an algebraic base
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
OA_place: publisher
OA_type: gold
_id: '20253'
abstract:
- lang: eng
  text: "A quantitative word automaton (QWA) defines a function from infinite words
    to values. For example, every infinite run of a limit-average QWA \U0001D49C obtains
    a mean payoff, and every word w ∈ Σ^ω is assigned the maximal mean payoff obtained
    by nondeterministic runs of \U0001D49C over w. We introduce quantitative language
    automata (QLAs) that define functions from language generators (i.e., implementations)
    to values, where a language generator can be nonprobabilistic, defining a set
    of infinite words, or probabilistic, defining a probability measure over infinite
    words. A QLA consists of a QWA and an aggregator function. For example, given
    a QWA \U0001D49C, the infimum aggregator maps each language L ⊆ Σ^ω to the greatest
    lower bound assigned by \U0001D49C to any word in L. For boolean value sets, QWAs
    define boolean properties of traces, and QLAs define boolean properties of sets
    of traces, i.e., hyperproperties. For more general value sets, QLAs serve as a
    specification language for a generalization of hyperproperties, called quantitative
    hyperproperties. A nonprobabilistic (resp. probabilistic) quantitative hyperproperty
    assigns a value to each set (resp. distribution) G of traces, e.g., the minimal
    (resp. expected) average response time exhibited by the traces in G. We give several
    examples of quantitative hyperproperties and investigate three paradigmatic problems
    for QLAs: evaluation, nonemptiness, and universality. In the evaluation problem,
    given a QLA \U0001D538 and an implementation G, we ask for the value that \U0001D538
    assigns to G. In the nonemptiness (resp. universality) problem, given a QLA \U0001D538
    and a value k, we ask whether \U0001D538 assigns at least k to some (resp. every)
    language. We provide a comprehensive picture of decidability for these problems
    for QLAs with common aggregators as well as their restrictions to ω-regular languages
    and trace distributions generated by finite-state Markov chains."
acknowledgement: This work was supported in part by the ERC-2020-AdG 101020093.
alternative_title:
- LIPIcs
article_number: '21'
article_processing_charge: No
arxiv: 1
author:
- first_name: Thomas A
  full_name: Henzinger, Thomas A
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000-0002-2985-7724
- first_name: Pavol
  full_name: Kebis, Pavol
  id: 2e0132b3-4e98-11ef-b275-cf7281c2802a
  last_name: Kebis
- first_name: Nicolas Adrien
  full_name: Mazzocchi, Nicolas Adrien
  id: b26baa86-3308-11ec-87b0-8990f34baa85
  last_name: Mazzocchi
- first_name: Naci E
  full_name: Sarac, Naci E
  id: 8C6B42F8-C8E6-11E9-A03A-F2DCE5697425
  last_name: Sarac
citation:
  ama: 'Henzinger TA, Kebis P, Mazzocchi NA, Sarac NE. Quantitative language automata.
    In: <i>36th International Conference on Concurrency Theory</i>. Vol 348. Schloss
    Dagstuhl - Leibniz-Zentrum für Informatik; 2025. doi:<a href="https://doi.org/10.4230/LIPIcs.CONCUR.2025.21">10.4230/LIPIcs.CONCUR.2025.21</a>'
  apa: 'Henzinger, T. A., Kebis, P., Mazzocchi, N. A., &#38; Sarac, N. E. (2025).
    Quantitative language automata. In <i>36th International Conference on Concurrency
    Theory</i> (Vol. 348). Aarhus, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für
    Informatik. <a href="https://doi.org/10.4230/LIPIcs.CONCUR.2025.21">https://doi.org/10.4230/LIPIcs.CONCUR.2025.21</a>'
  chicago: Henzinger, Thomas A, Pavol Kebis, Nicolas Adrien Mazzocchi, and Naci E
    Sarac. “Quantitative Language Automata.” In <i>36th International Conference on
    Concurrency Theory</i>, Vol. 348. Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
    2025. <a href="https://doi.org/10.4230/LIPIcs.CONCUR.2025.21">https://doi.org/10.4230/LIPIcs.CONCUR.2025.21</a>.
  ieee: T. A. Henzinger, P. Kebis, N. A. Mazzocchi, and N. E. Sarac, “Quantitative
    language automata,” in <i>36th International Conference on Concurrency Theory</i>,
    Aarhus, Denmark, 2025, vol. 348.
  ista: 'Henzinger TA, Kebis P, Mazzocchi NA, Sarac NE. 2025. Quantitative language
    automata. 36th International Conference on Concurrency Theory. CONCUR: Conference
    on Concurrency Theory, LIPIcs, vol. 348, 21.'
  mla: Henzinger, Thomas A., et al. “Quantitative Language Automata.” <i>36th International
    Conference on Concurrency Theory</i>, vol. 348, 21, Schloss Dagstuhl - Leibniz-Zentrum
    für Informatik, 2025, doi:<a href="https://doi.org/10.4230/LIPIcs.CONCUR.2025.21">10.4230/LIPIcs.CONCUR.2025.21</a>.
  short: T.A. Henzinger, P. Kebis, N.A. Mazzocchi, N.E. Sarac, in:, 36th International
    Conference on Concurrency Theory, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
    2025.
conference:
  end_date: 2025-08-29
  location: Aarhus, Denmark
  name: 'CONCUR: Conference on Concurrency Theory'
  start_date: 2025-08-26
corr_author: '1'
date_created: 2025-08-31T22:01:32Z
date_published: 2025-08-18T00:00:00Z
date_updated: 2025-12-01T12:36:52Z
day: '18'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.4230/LIPIcs.CONCUR.2025.21
ec_funded: 1
external_id:
  arxiv:
  - '2506.0515'
  isi:
  - '001570540800021'
file:
- access_level: open_access
  checksum: 9d4054058757a73477e6015b10ed6996
  content_type: application/pdf
  creator: dernst
  date_created: 2025-09-03T10:01:53Z
  date_updated: 2025-09-03T10:01:53Z
  file_id: '20282'
  file_name: 2025_CONCUR_HenzingerT.pdf
  file_size: 1257397
  relation: main_file
  success: 1
file_date_updated: 2025-09-03T10:01:53Z
fulldoi: https://doi.org/10.4230/LIPIcs.CONCUR.2025.21
has_accepted_license: '1'
intvolume: '       348'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 62781420-2b32-11ec-9570-8d9b63373d4d
  call_identifier: H2020
  grant_number: '101020093'
  name: Vigilant Algorithmic Monitoring of Software
publication: 36th International Conference on Concurrency Theory
publication_identifier:
  isbn:
  - '9783959773898'
  issn:
  - 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantitative language automata
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 348
year: '2025'
...