{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T10:10:01Z","timestamp":1723198201069},"reference-count":0,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["VLSI Design"],"published-print":{"date-parts":[[2002,1]]},"abstract":"<jats:p>A new algorithm for the identification of disjoint bi\u2010decomposition in Boolean functions from its Walsh spectrum is proposed. The type of bi\u2010decomposition and its existence is derived from the knowledge of a subset of Walsh spectrum for a Boolean function. All three types of bi\u2010decomposition are considered including OR, AND and EXOR type. A filtering procedure that uses just few Walsh spectral coefficients (SC) is applied to quickly eliminate the functions that are not bi\u2010decomposable and hence the algorithm is very efficient. The type of bi\u2010decomposition and affirmation\/negation of variables in its logic sub\u2010functions are directly identified by manipulation on the reduced cubical representation of Boolean functions and their corresponding Walsh spectra. The presented algorithm has been implemented in C and tested on the standard benchmark functions. The number of Boolean functions having various disjoint bi\u2010decompositions has also been enumerated.<\/jats:p>","DOI":"10.1080\/10655140290011104","type":"journal-article","created":{"date-parts":[[2002,9,30]],"date-time":"2002-09-30T17:08:06Z","timestamp":1033405686000},"page":"307-313","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Identification of Disjoint Bi\u2010decompositions in Boolean Functions through Walsh Spectrum"],"prefix":"10.1155","volume":"14","author":[{"given":"Bogdan J.","family":"Falkowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sudha","family":"Kannurao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2000,8,10]]},"container-title":["VLSI Design"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/2002\/349538.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1080\/10655140290011104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T09:48:30Z","timestamp":1723196910000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1080\/10655140290011104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,8,10]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["10.1080\/10655140290011104"],"URL":"https:\/\/doi.org\/10.1080\/10655140290011104","archive":["Portico"],"relation":{},"ISSN":["1065-514X","1563-5171"],"issn-type":[{"type":"print","value":"1065-514X"},{"type":"electronic","value":"1563-5171"}],"subject":[],"published":{"date-parts":[[2000,8,10]]},"assertion":[{"value":"2000-05-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2000-08-10","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}