The complexity of Boolean functions in the Reed–Muller polynomials class
This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functio...
Gespeichert in:
Veröffentlicht in: | Automatic control and computer sciences 2017, Vol.51 (5), p.285-293 |
---|---|
1. Verfasser: | |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 293 |
---|---|
container_issue | 5 |
container_start_page | 285 |
container_title | Automatic control and computer sciences |
container_volume | 51 |
creator | Suprun, V. P. |
description | This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functions of
n
variables whose complexity (in terms of the number of terms) coincides with value. We investigate the properties of functions and propose their schematic realization on elements AND, XOR, and NAND. |
doi_str_mv | 10.3103/S0146411617050078 |
format | Article |
fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1965286016</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1965286016</sourcerecordid><originalsourceid>FETCH-LOGICAL-c268t-3319bae2d42910af1ef3e4d34f409c5011ef1b1d65d91c175ce26fe960fa6963</originalsourceid><addsrcrecordid>eNp1kM9KxDAQxoMouK4-gLeA5-pM02Sboy7-ZUXQPXgr3XSiXbpNTVqwN9_BN_RJbFkPgngaZr7f9w18jB0jnAoEcfYEmKgEUeEMJMAs3WETlDKNENLnXTYZ5WjU99lBCGuAQUvVhN0tX4kbt2kqei_bnjvLL5yrKK-57WrTlq4OvKx5O2CPRMXXx-d9V1XkeeOqvnabMq8CN1UewiHbs8NCRz9zypZXl8v5TbR4uL6dny8iE6u0jYRAvcopLpJYI-QWyQpKCpHYBLSRgMMBV1goWWg0OJOGYmVJK7C50kpM2ck2tvHuraPQZmvX-Xr4mKFWMk4V4EjhljLeheDJZo0vN7nvM4RsbCz709jgibeeMLD1C_lfyf-avgFap22r</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1965286016</pqid></control><display><type>article</type><title>The complexity of Boolean functions in the Reed–Muller polynomials class</title><source>SpringerLink Journals - AutoHoldings</source><creator>Suprun, V. P.</creator><creatorcontrib>Suprun, V. P.</creatorcontrib><description>This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functions of
n
variables whose complexity (in terms of the number of terms) coincides with value. We investigate the properties of functions and propose their schematic realization on elements AND, XOR, and NAND.</description><identifier>ISSN: 0146-4116</identifier><identifier>EISSN: 1558-108X</identifier><identifier>DOI: 10.3103/S0146411617050078</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Boolean algebra ; Boolean functions ; Codes ; Complexity ; Computer Science ; Control Structures and Microprogramming ; Functions (mathematics) ; Mathematical analysis ; Polynomials</subject><ispartof>Automatic control and computer sciences, 2017, Vol.51 (5), p.285-293</ispartof><rights>Allerton Press, Inc. 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.3103/S0146411617050078$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.3103/S0146411617050078$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Suprun, V. P.</creatorcontrib><title>The complexity of Boolean functions in the Reed–Muller polynomials class</title><title>Automatic control and computer sciences</title><addtitle>Aut. Control Comp. Sci</addtitle><description>This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functions of
n
variables whose complexity (in terms of the number of terms) coincides with value. We investigate the properties of functions and propose their schematic realization on elements AND, XOR, and NAND.</description><subject>Boolean algebra</subject><subject>Boolean functions</subject><subject>Codes</subject><subject>Complexity</subject><subject>Computer Science</subject><subject>Control Structures and Microprogramming</subject><subject>Functions (mathematics)</subject><subject>Mathematical analysis</subject><subject>Polynomials</subject><issn>0146-4116</issn><issn>1558-108X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kM9KxDAQxoMouK4-gLeA5-pM02Sboy7-ZUXQPXgr3XSiXbpNTVqwN9_BN_RJbFkPgngaZr7f9w18jB0jnAoEcfYEmKgEUeEMJMAs3WETlDKNENLnXTYZ5WjU99lBCGuAQUvVhN0tX4kbt2kqei_bnjvLL5yrKK-57WrTlq4OvKx5O2CPRMXXx-d9V1XkeeOqvnabMq8CN1UewiHbs8NCRz9zypZXl8v5TbR4uL6dny8iE6u0jYRAvcopLpJYI-QWyQpKCpHYBLSRgMMBV1goWWg0OJOGYmVJK7C50kpM2ck2tvHuraPQZmvX-Xr4mKFWMk4V4EjhljLeheDJZo0vN7nvM4RsbCz709jgibeeMLD1C_lfyf-avgFap22r</recordid><startdate>2017</startdate><enddate>2017</enddate><creator>Suprun, V. P.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2017</creationdate><title>The complexity of Boolean functions in the Reed–Muller polynomials class</title><author>Suprun, V. P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-3319bae2d42910af1ef3e4d34f409c5011ef1b1d65d91c175ce26fe960fa6963</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Boolean algebra</topic><topic>Boolean functions</topic><topic>Codes</topic><topic>Complexity</topic><topic>Computer Science</topic><topic>Control Structures and Microprogramming</topic><topic>Functions (mathematics)</topic><topic>Mathematical analysis</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Suprun, V. P.</creatorcontrib><collection>CrossRef</collection><jtitle>Automatic control and computer sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Suprun, V. P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The complexity of Boolean functions in the Reed–Muller polynomials class</atitle><jtitle>Automatic control and computer sciences</jtitle><stitle>Aut. Control Comp. Sci</stitle><date>2017</date><risdate>2017</risdate><volume>51</volume><issue>5</issue><spage>285</spage><epage>293</epage><pages>285-293</pages><issn>0146-4116</issn><eissn>1558-108X</eissn><abstract>This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functions of
n
variables whose complexity (in terms of the number of terms) coincides with value. We investigate the properties of functions and propose their schematic realization on elements AND, XOR, and NAND.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.3103/S0146411617050078</doi><tpages>9</tpages></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0146-4116 |
ispartof | Automatic control and computer sciences, 2017, Vol.51 (5), p.285-293 |
issn | 0146-4116 1558-108X |
language | eng |
recordid | cdi_proquest_journals_1965286016 |
source | SpringerLink Journals - AutoHoldings |
subjects | Boolean algebra Boolean functions Codes Complexity Computer Science Control Structures and Microprogramming Functions (mathematics) Mathematical analysis Polynomials |
title | The complexity of Boolean functions in the Reed–Muller polynomials class |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-12T19%3A32%3A10IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20complexity%20of%20Boolean%20functions%20in%20the%20Reed%E2%80%93Muller%20polynomials%20class&rft.jtitle=Automatic%20control%20and%20computer%20sciences&rft.au=Suprun,%20V.%20P.&rft.date=2017&rft.volume=51&rft.issue=5&rft.spage=285&rft.epage=293&rft.pages=285-293&rft.issn=0146-4116&rft.eissn=1558-108X&rft_id=info:doi/10.3103/S0146411617050078&rft_dat=%3Cproquest_cross%3E1965286016%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1965286016&rft_id=info:pmid/&rfr_iscdi=true |