[{"year":"2026","has_accepted_license":"1","publication_status":"epub_ahead","date_published":"2026-07-10T00:00:00Z","researchdata_availability":"no","title":"Transcendence for Pisot morphic words over an algebraic base","author":[{"full_name":"Kebis, Pavol","id":"2e0132b3-4e98-11ef-b275-cf7281c2802a","first_name":"Pavol","last_name":"Kebis"},{"full_name":"LUCA, FLORIAN","last_name":"LUCA","first_name":"FLORIAN"},{"last_name":"OUAKNINE","first_name":"JOEL","full_name":"OUAKNINE, JOEL"},{"first_name":"ANDREW","last_name":"SCOONES","full_name":"SCOONES, ANDREW"},{"first_name":"JAMES","last_name":"WORRELL","full_name":"WORRELL, JAMES"}],"publisher":"Cambridge University Press","article_processing_charge":"Yes (in subscription journal)","mathsc":["11J81","37B10","11J87"],"_id":"22406","keyword":["balanced-pair algorithm","Cobham’s conjecture","k-Bonacci words","Pisot conjecture","subspace theorem"],"das_tickbox":"0","quality_controlled":"1","external_id":{"arxiv":["2405.05279"]},"status":"public","license":"https://creativecommons.org/licenses/by/4.0/","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.","language":[{"iso":"eng"}],"abstract":[{"text":"It is known that for a uniform morphic sequence 𝒖 =⟨𝑢𝑛⟩∞\r\n𝑛=0 and an algebraic number 𝛽 such that |𝛽| >1, the number [[𝒖]]𝛽 :=∑∞\r\n𝑛=0(𝑢𝑛/𝛽𝑛) either lies in ℚ⁡(𝛽) 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 [[𝒖]]𝛽 outright. In particular, for 𝑘 ≥2, if 𝒖 is the k-Bonacci word, then [[𝒖]]𝛽 is transcendental.","lang":"eng"}],"publication":"Ergodic Theory and Dynamical Systems","date_updated":"2026-08-03T06:17:50Z","date_created":"2026-07-27T05:53:25Z","doi":"10.1017/etds.2026.10324","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","ddc":["000"],"month":"07","page":"1-22","type":"journal_article","supplementarymaterial":"no","department":[{"_id":"ToHe"},{"_id":"GradSch"}],"OA_place":"publisher","oa":1,"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/etds.2026.10324"}],"fulldoi":"https://doi.org/10.1017/etds.2026.10324","citation":{"short":"P. Kebis, F. LUCA, J. OUAKNINE, A. SCOONES, J. WORRELL, Ergodic Theory and Dynamical Systems (2026) 1–22.","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>.","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.","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>","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.","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>.","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>"},"publication_identifier":{"issn":["0143-3857"],"eissn":["1469-4417"]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"day":"10","OA_type":"hybrid","article_type":"original","PlanS_conform":"1"},{"day":"18","OA_type":"gold","file_date_updated":"2025-09-03T10:01:53Z","file":[{"access_level":"open_access","success":1,"content_type":"application/pdf","creator":"dernst","checksum":"9d4054058757a73477e6015b10ed6996","file_size":1257397,"file_name":"2025_CONCUR_HenzingerT.pdf","file_id":"20282","relation":"main_file","date_created":"2025-09-03T10:01:53Z","date_updated":"2025-09-03T10:01:53Z"}],"citation":{"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>","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.","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>.","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>","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.","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>.","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."},"fulldoi":"https://doi.org/10.4230/LIPIcs.CONCUR.2025.21","publication_identifier":{"isbn":["9783959773898"],"issn":["1868-8969"]},"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"OA_place":"publisher","scopus_import":"1","oa":1,"type":"conference","department":[{"_id":"ToHe"}],"ec_funded":1,"project":[{"grant_number":"101020093","call_identifier":"H2020","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","name":"Vigilant Algorithmic Monitoring of Software"}],"arxiv":1,"conference":{"end_date":"2025-08-29","location":"Aarhus, Denmark","name":"CONCUR: Conference on Concurrency Theory","start_date":"2025-08-26"},"corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["000"],"oa_version":"Published Version","month":"08","date_updated":"2025-12-01T12:36:52Z","doi":"10.4230/LIPIcs.CONCUR.2025.21","date_created":"2025-08-31T22:01:32Z","publication":"36th International Conference on Concurrency Theory","volume":348,"language":[{"iso":"eng"}],"acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093.","status":"public","intvolume":"       348","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 𝒜 obtains a mean payoff, and every word w ∈ Σ^ω is assigned the maximal mean payoff obtained by nondeterministic runs of 𝒜 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 𝒜, the infimum aggregator maps each language L ⊆ Σ^ω to the greatest lower bound assigned by 𝒜 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 𝔸 and an implementation G, we ask for the value that 𝔸 assigns to G. In the nonemptiness (resp. universality) problem, given a QLA 𝔸 and a value k, we ask whether 𝔸 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."}],"quality_controlled":"1","alternative_title":["LIPIcs"],"external_id":{"isi":["001570540800021"],"arxiv":["2506.0515"]},"article_number":"21","article_processing_charge":"No","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","_id":"20253","title":"Quantitative language automata","author":[{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","full_name":"Henzinger, Thomas A","orcid":"0000-0002-2985-7724","first_name":"Thomas A","last_name":"Henzinger"},{"first_name":"Pavol","last_name":"Kebis","full_name":"Kebis, Pavol","id":"2e0132b3-4e98-11ef-b275-cf7281c2802a"},{"full_name":"Mazzocchi, Nicolas Adrien","id":"b26baa86-3308-11ec-87b0-8990f34baa85","first_name":"Nicolas Adrien","last_name":"Mazzocchi"},{"last_name":"Sarac","first_name":"Naci E","full_name":"Sarac, Naci E","id":"8C6B42F8-C8E6-11E9-A03A-F2DCE5697425"}],"date_published":"2025-08-18T00:00:00Z","year":"2025","has_accepted_license":"1","publication_status":"published","isi":1}]