{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:40:57Z","timestamp":1753890057472,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,8,7]],"date-time":"2017-08-07T00:00:00Z","timestamp":1502064000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,8,7]],"date-time":"2017-08-07T00:00:00Z","timestamp":1502064000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,8,7]],"date-time":"2017-08-07T00:00:00Z","timestamp":1502064000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["658162"],"award-info":[{"award-number":["658162"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of the left-hand sides; the computational intuition is that rules cannot build new data structures. In programming language research, cons-free languages have been used to characterize hierarchies of computational complexity classes; in term rewriting, cons-free first-order TRSs have been used to characterize the class PTIME.   We investigate cons-free higher-order term rewriting systems, the complexity classes they characterize, and how these depend on the type order of the systems. We prove that, for every K $\\geq$ 1, left-linear cons-free systems with type order K characterize E$^K$TIME if unrestricted evaluation is used (i.e., the system does not have a fixed reduction strategy).   The main difference with prior work in implicit complexity is that (i) our results hold for non-orthogonal term rewriting systems with no assumptions on reduction strategy, (ii) we consequently obtain much larger classes for each type order (E$^K$TIME versus EXP$^{K-1}$TIME), and (iii) results for cons-free term rewriting systems have previously only been obtained for K = 1, and with additional syntactic restrictions besides cons-freeness and left-linearity.   Our results are among the first implicit characterizations of the hierarchy E = E$^1$TIME $\\subsetneq$ E$^2$TIME $\\subsetneq$ ... Our work confirms prior results that having full non-determinism (via overlapping rules) does not directly allow for characterization of non-deterministic complexity classes like NE. We also show that non-determinism makes the classes characterized highly sensitive to minor syntactic changes like admitting product types or non-left-linear rules.<\/jats:p><jats:p>Comment: extended version of a paper submitted to FSCD 2016. arXiv admin note:   substantial text overlap with arXiv:1604.08936<\/jats:p>","DOI":"10.23638\/lmcs-13(3:8)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:29:06Z","timestamp":1743701346000},"source":"Crossref","is-referenced-by-count":0,"title":["Complexity Hierarchies and Higher-order Cons-free Term Rewriting"],"prefix":"10.23638","volume":"Volume 13, Issue 3","author":[{"given":"Cynthia","family":"Kop","sequence":"first","affiliation":[]},{"given":"Jakob Grue","family":"Simonsen","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,8,7]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1611.10334v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1611.10334v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:29:06Z","timestamp":1743701346000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/2573"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,7]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(3:8)2017","relation":{"has-preprint":[{"id-type":"arxiv","id":"1611.10334v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1611.10334v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1611.10334","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1611.10334","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2017,8,7]]},"article-number":"2573"}}