{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T20:32:30Z","timestamp":1672432350227},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[1994,9]]},"abstract":"<jats:p> This paper presents the main concepts of the mathematical theory PEI for parallel programming and emphasizes its derivation power. The mathematical basis of this theory leads to a nice implementation in CENTAUR<jats:sup>7<\/jats:sup> of an environment whose purpose is to transform parallel programs. It is illustrated by two similar examples: the convolution sum and the Dirichlet product. The second one uses non-affine dependencies that can be easily taken into account using PEI. <\/jats:p>","DOI":"10.1142\/s0129626494000296","type":"journal-article","created":{"date-parts":[[2004,11,18]],"date-time":"2004-11-18T21:21:13Z","timestamp":1100812873000},"page":"313-328","source":"Crossref","is-referenced-by-count":3,"title":["A MATHEMATICAL THEORY AND ITS ENVIRONMENT FOR PARALLEL PROGRAMMING"],"prefix":"10.1142","volume":"04","author":[{"given":"ERIC","family":"VIOLARD","sequence":"first","affiliation":[{"name":"University of Franche-Comt\u00e9, Laboratoire d\u2019Informatique, F-25030 Besan\u00e7on cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626494000296","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:17:49Z","timestamp":1565093869000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626494000296"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,9]]},"references-count":0,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[1994,9]]}},"alternative-id":["10.1142\/S0129626494000296"],"URL":"https:\/\/doi.org\/10.1142\/s0129626494000296","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"value":"0129-6264","type":"print"},{"value":"1793-642X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,9]]}}}