{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:19:16Z","timestamp":1777645156455,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T00:00:00Z","timestamp":1555459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2019,4,17]]},"abstract":"<jats:p>\n                    We introduce word matrices and word matrix rewriting systems. A word matrix over an alphabet \u2211 of k letters is a k \u00d7 n rectangular matrix with entries of nonnegative integers. A word matrix represents a set of words. The i-th row corresponds to the i-th letter in \u2211 (thus the letters in \u2211 are ordered as a\n                    <jats:sub>1<\/jats:sub>\n                    , . . . , a\n                    <jats:sub>k<\/jats:sub>\n                    ). Each column vector represents a set of words which have the vector as the Parikh vector. The word matrix represents the concatenation of all sets represented by column vectors. A word matrix rewriting system consists of a set of rewriting rules which rewrite word matrices and an initial word matrix (the axiom). A word matrix rewriting system generates a set of word matrices by iterated applications of rules to the axiom and generates a language which is the union of all sets represented by the matrices. A word matrix rewriting system is a kind of (restricted) parallel rewriting system with scattered context dependency and hence can generate non-context-free languages, e.g., { a\n                    <jats:sup>n<\/jats:sup>\n                    b\n                    <jats:sup>n<\/jats:sup>\n                    c\n                    <jats:sup>n<\/jats:sup>\n                    | 1 \u2264 n}. We define variants of word matrix rewriting systems and show an infinite hierarchy among them. Some language theoretical problems, including relations among Chomsky hierarchy, closure properties, and decision properties, are considered.\n                  <\/jats:p>","DOI":"10.3233\/fi-2019-1800","type":"journal-article","created":{"date-parts":[[2019,4,19]],"date-time":"2019-04-19T10:50:30Z","timestamp":1555671030000},"page":"199-226","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Word Matrix Rewriting Systems"],"prefix":"10.1177","volume":"166","author":[{"given":"Raj Kishor","family":"Bisht","sequence":"first","affiliation":[{"name":"Department of Applied Sciences, Amrapali Institute of Technology and Sciences, Lamachaur, Haldwani, (Nainital) Uttarakhand 263139, India."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Taishin Yasunobu","family":"Nishida","sequence":"additional","affiliation":[{"name":"Department of Information Systems, Toyama Prefectural University, Imizu 939-0398, Japan."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kouhei","family":"Yamamoto","sequence":"additional","affiliation":[{"name":"Department of Information Systems, Toyama Prefectural University, Imizu 939-0398, Japan."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,4,17]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2019-1800","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2019-1800","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:29Z","timestamp":1777444289000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2019-1800"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,17]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,4,17]]}},"alternative-id":["10.3233\/FI-2019-1800"],"URL":"https:\/\/doi.org\/10.3233\/fi-2019-1800","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,17]]}}}