{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T16:11:47Z","timestamp":1762359107418,"version":"build-2065373602"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,8,6]]},"abstract":"<jats:p>The class of type-two basic feasible functionals ($\\mathtt{BFF}_2$) is the analogue of $\\mathtt{FP}$ (polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments. $\\mathtt{BFF}_2$ can be defined through Oracle Turing machines with running time bounded by second-order polynomials. On the other hand, higher-order term rewriting provides an elegant formalism for expressing higher-order computation. We address the problem of characterizing $\\mathtt{BFF}_2$ by higher-order term rewriting. Various kinds of interpretations for first-order term rewriting have been introduced in the literature for proving termination and characterizing first-order complexity classes. In this paper, we consider a recently introduced notion of cost-size interpretations for higher-order term rewriting and see second order rewriting as ways of computing type-2 functionals. We then prove that the class of functionals represented by higher-order terms admitting polynomially bounded cost-size interpretations exactly corresponds to $\\mathtt{BFF}_2$.<\/jats:p>","DOI":"10.46298\/lmcs-21(4:19)2025","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T16:10:06Z","timestamp":1762359006000},"source":"Crossref","is-referenced-by-count":0,"title":["A Characterization of Basic Feasible Functionals Through Higher-Order Rewriting and Tuple Interpretations"],"prefix":"10.46298","volume":"Volume 21, Issue 4","author":[{"given":"Patrick","family":"Baillot","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ugo Dal","family":"Lago","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cynthia","family":"Kop","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deivid","family":"Vale","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2025,11,5]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2401.12385v6","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2401.12385v6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T16:10:06Z","timestamp":1762359006000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/14655"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,5]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(4:19)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2401.12385v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2401.12385v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2401.12385","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2401.12385","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,5]]},"article-number":"14655"}}