{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:24:05Z","timestamp":1777645445972,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["FI"],"published-print":{"date-parts":[[2021,1,13]]},"abstract":"<jats:p>Higher-Order Fixpoint Logic (HFL) is a modal specification language whose expressive power reaches far beyond that of Monadic Second-Order Logic, achieved through an incorporation of a typed \u03bb-calculus into the modal \u03bc-calculus. Its model checking problem on finite transition systems is decidable, albeit of high complexity, namely k-EXPTIME-complete for formulas that use functions of type order at most k &lt; 0. In this paper we present a fragment with a presumably easier model checking problem. We show that so-called tail-recursive formulas of type order k can be model checked in (k \u2212 1)-EXPSPACE, and also give matching lower bounds. This yields generic results for the complexity of bisimulation-invariant non-regular properties, as these can typically be defined in HFL.<\/jats:p>","DOI":"10.3233\/fi-2021-1996","type":"journal-article","created":{"date-parts":[[2021,1,15]],"date-time":"2021-01-15T12:18:08Z","timestamp":1610713088000},"page":"1-30","source":"Crossref","is-referenced-by-count":3,"title":["The Complexity of Model-Checking Tail-Recursive Higher-Order Fixpoint Logic"],"prefix":"10.1177","volume":"178","author":[{"given":"Florian","family":"Bruse","sequence":"first","affiliation":[{"name":"University of Kassel, Kassel, Germany. florian.bruse@uni-kassel.de, martin.lange@uni-kassel.de"}]},{"given":"Martin","family":"Lange","sequence":"additional","affiliation":[{"name":"University of Kassel, Kassel, Germany. florian.bruse@uni-kassel.de, martin.lange@uni-kassel.de"}]},{"given":"Etienne","family":"Lozes","sequence":"additional","affiliation":[{"name":"University of Nice Sophia Antipolis, I3S, CNRS, France. etienne.lozes@unice.fr"}]}],"member":"179","container-title":["Fundamenta Informaticae"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/FI-2021-1996","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:32:14Z","timestamp":1777444334000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/FI-2021-1996"}},"subtitle":[],"editor":[{"given":"Matthew","family":"Hague","sequence":"additional","affiliation":[]},{"given":"Igor","family":"Potapov","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1,13]]},"references-count":0,"journal-issue":{"issue":"1-2"},"URL":"https:\/\/doi.org\/10.3233\/fi-2021-1996","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,13]]}}}