Editing Quine–McCluskey algorithm (section)

==References==
{{reflist|refs=
<ref name="Quine_1952">{{cite journal |last=Quine |first=Willard Van Orman |author-link=Willard Van Orman Quine |date=October 1952 |title=The Problem of Simplifying Truth Functions |jstor=2308219 |journal=[[The American Mathematical Monthly]] |volume=59 |issue=8 |pages=521–531 |doi=10.2307/2308219}}</ref>
<ref name="Quine_1955">{{cite journal |last=Quine |first=Willard Van Orman |author-link=Willard Van Orman Quine |date=November 1955 |title=A Way to Simplify Truth Functions |jstor=2307285 |journal=[[The American Mathematical Monthly]] |volume=62 |issue=9 |pages=627–631 |doi=10.2307/2307285 |hdl=10338.dmlcz/142789}}</ref>
<ref name="McCluskey_1956">{{cite journal |last=McCluskey |first=Edward Joseph Jr.|author-link=Edward Joseph McCluskey, Jr. |date=November 1956 |title=Minimization of Boolean Functions |journal=[[Bell System Technical Journal]] |volume=35 |issue=6 |pages=1417–1444 |doi=10.1002/j.1538-7305.1956.tb03835.x |url=https://archive.org/details/bstj35-6-1417 |access-date=2014-08-24 |hdl=10338.dmlcz/102933}}</ref>
<ref name="Nelson_1995">{{cite book |last1=Nelson |first1=Victor P. |first2=H. Troy |last2=Nagle |first3=Bill D. |last3=Carroll |first4=J. David |last4=Irwin |author-link4=J. David Irwin |date=1995 |title=Digital Logic Circuit Analysis and Design |url=https://books.google.com/books?id=8V5TAAAAMAAJ |publisher=[[Prentice Hall]] |page=234 |edition=2 |access-date=2014-08-26 |isbn=978-0-13463894-2}}</ref>
<ref name="Logic_Friday">[[Logic Friday]] program</ref>
<ref name="Masek_1979">{{cite book |first=William J. |last=Masek |title=Some NP-complete set covering problems |publisher=unpublished |date=1979}}</ref>
<ref name="Czort_1999">{{cite thesis |type=Master's thesis |first=Sebastian Lukas Arne |last=Czort |title=The complexity of minimizing disjunctive normal form formulas |institution=University of Aarhus |date=1999}}</ref>
<ref name="Umans_2006">{{cite journal |first1=Christopher |last1=Umans |author-link1=Christopher Umans |first2=Tiziano |last2=Villa |first3=Alberto Luigi |last3=Sangiovanni-Vincentelli |author-link3=Alberto Luigi Sangiovanni-Vincentelli |title=Complexity of two-level logic minimization |journal=[[IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems]] |volume=25 |number=7 |pages=1230–1246 |date=2006-06-05 |doi=10.1109/TCAD.2005.855944 |s2cid=10187481}}</ref>
<ref name="Feldman_2009">{{cite journal |first=Vitaly |last=Feldman |title=Hardness of Approximate Two-Level Logic Minimization and PAC Learning with Membership Queries |journal=[[Journal of Computer and System Sciences]] |volume=75 |pages=13–25 [13–14] |date=2009 |doi=10.1016/j.jcss.2008.07.007|doi-access=free }}</ref>
<ref name="Gimpel_1965">{{cite journal |first=James F. |last=Gimpel |title=A Method for Producing a Boolean Function Having an Arbitrary Prescribed Prime Implicant Table |journal=[[IEEE Transactions on Computers]] |volume=14 |pages=485–488 |date=1965 |doi=10.1109/PGEC.1965.264175}}</ref>
<ref name="Paul_1974">{{cite journal |first=Wolfgang Jakob |last=Paul |author-link=:de:Wolfgang Paul (Informatiker) |title=Boolesche Minimalpolynome und Überdeckungsprobleme |language=de |journal=[[Acta Informatica]] |volume=4 |issue=4 |pages=321–336 |date=1974 |doi=10.1007/BF00289615 |s2cid=35973949}}</ref>
<ref name="Abrahams_Nordahl_1955">{{cite book |first1=Paul William |last1=Abrahams |first2=John "Jack" G. |last2=Nordahl |title=The Modified Quine–McCluskey Reduction Procedure |date=November 1955 |location=Electrical Engineering Department, [[Massachusetts Institute of Technology]], Massachusetts, USA |type=Class memorandum}} (4 pages) (NB. Some sources list the authors as "{{citeref|Caldwell|1958|P. W. Abraham|style=plain}}"<!-- without pending "s", forenames unconfirmed --> and "{{citeref|Kämmerer|1969|I.<!-- rather than J. --> G. Nordahl|style=plain}}", the title is also cited as "{{citeref|Caldwell|1958|Modified McCluskey–Quine Reduction Procedure|style=plain}}".<!-- added "the", swapped order of names -->)<!-- [https://web.archive.org/web/20200815142344/https://www.chessprogramming.org/Paul_W._Abrahams] [https://web.archive.org/web/20200509033309/https://www.informit.com/authors/bio/33d9a1db-dae1-4ec3-bae5-406f84184012][https://web.archive.org/web/20200509034657/https://dl.acm.org/doi/pdf/10.1145/1141880.1380529] --></ref>
<ref name="Nordahl_2017">{{cite web |title=Welcome to the memorial page for John "Jack" G Nordahl June 14, 1933 ~ November 20, 2017 (age 84) |publisher=Jellison Funeral Home and Cremation Services |url=https://www.jellisonfuneralhome.com/obituary/JohnJack-Nordahl |access-date=2020-05-05 |url-status=live |archive-url=https://web.archive.org/web/20200505151004/https://www.jellisonfuneralhome.com/obituary/JohnJack-Nordahl |archive-date=2020-05-05}}</ref>
<ref name="Caldwell_1958">{{cite book |title=Switching Circuits and Logical Design |chapter=5.8. Operations Using Decimal Symbols |first=Samuel Hawks |last=Caldwell |author-link=Samuel Hawks Caldwell |version=5th printing September 1963 |date=1958-12-01 |orig-date=February 1958 |edition=1st |publisher=[[John Wiley & Sons Inc.]] |publication-place=New York, USA |location=Watertown, Massachusetts, USA |isbn=0-47112969-0 |lccn=58-7896 |pages=162–169 |quote-page=166 |quote=[...] It is a pleasure to record that this treatment is based on the work of two students during the period they were studying Switching Circuits at the Massachusetts Institute of Technology. They discussed the method independently and then collaborated in preparing a class memorandum: {{citeref|Abrahams|Nordahl|1955|P. W. Abraham and J. G. Nordahl|style=plain}} [...]}} (xviii+686 pages) (NB. For the first major treatise of the decimal method in this book, it is sometimes misleadingly known as "Caldwell's decimal tabulation".)</ref>
<ref name="Mullin_Kellner_1958">{{cite journal |title=A Residue Test for Boolean Functions |first1=Albert Alkins |last1=Mullin |author-link1=Albert Alkins Mullin |first2=Wayne G. |last2=Kellner |journal=Transactions of the Illinois State Academy of Science |volume=51 |number=3–4 |date=1958<!-- |orig-date=November 1955 According to Caldwell --> |publication-place=Springfield, Illinois, USA |location=University of Illinois, Urbana, USA and Electrical Engineering Department, [[Massachusetts Institute of Technology]], Massachusetts, USA |type=Teaching memorandum |s2cid=125171479 |pages=14–19 |url=https://ilacadofsci.com/wp-content/uploads/2016/03/051-16-print.pdf |access-date=2020-05-05 |url-status=live |archive-url=https://web.archive.org/web/20200505163915/https://ilacadofsci.com/wp-content/uploads/2016/03/051-16-print.pdf |archive-date=2020-05-05}} [https://ilacadofsci.com/archives/9279] (6 pages) (NB. In {{citeref|Caldwell|1958|his book|style=plain}}, Caldwell dates this to November 1955 as a teaching memorandum. Since Mullin dates their work to 1958 in {{citeref|Mullin|1960|another work|style=plain}} and Abrahams/Nordahl's {{citeref|Abrahams|Nordahl|1955|class memorandum|style=plain}} is also dated November 1955, this could be a copy error.)</ref>
<ref name="Mullin_1959">{{cite journal |title=Two Applications of Elementary Number Theory |first=Albert Alkins |last=Mullin |author-link=Albert Alkins Mullin |journal=Transactions of the Illinois State Academy of Science |volume=52 |number=3–4 |date=1960-03-15 |orig-date=1959-09-19 |location=University of Illinois, Urbana, USA |publication-place=Springfield, Illinois, USA |editor-first1=Harvey I. |editor-last1=Fisher |editor-first2=George E. |editor-last2=Ekblaw |editor-first3=F. O. |editor-last3=Green |editor-first4=Reece |editor-last4=Jones |editor-first5=Francis |editor-last5=Kruidenier |editor-first6=John |editor-last6=McGregor |editor-first7=Paul |editor-last7=Silva |editor-first8=Milton |editor-last8=Thompson |pages=102–103 |url=https://ilacadofsci.com/wp-content/uploads/2016/03/052-15-print.pdf |access-date=2020-05-05 |url-status=live |archive-url=https://web.archive.org/web/20200505143916/https://ilacadofsci.com/wp-content/uploads/2016/03/052-15-print.pdf |archive-date=2020-05-05}} [https://ilacadofsci.com/archives/9203][https://archive.org/details/transactionsofil5219unse][https://archive.org/stream/transactionsofil5219unse/transactionsofil5219unse_djvu.txt] (2 pages)</ref>
<ref name="McCluskey_1960">{{cite journal |title=Albert A. Mullin and Wayne G. Kellner. A residue test for Boolean functions. Transactions of the Illinois State Academy of Science, vol. 51 nos. 3 and 4, (1958), pp. 14–19. |type=Review |last=McCluskey |first=Edward Joseph Jr.|author-link=Edward Joseph McCluskey, Jr. |journal=[[The Journal of Symbolic Logic]] |volume=25 |issue=2 |date=June 1960 |doi=10.2307/2964263 |page=185 |jstor=2964263 |s2cid=123530443 |quote-page=185 |quote=[...] The results of this paper are presented in the more readily available {{citeref|Caldwell|1958|book|style=plain}} by S. H. Caldwell [...<!-- XXIII 433 -->]. In this book, the author gives credit to {{citeref|Mullin|Kellner|1958|Mullin and Kellner|style=plain}} for development of the manipulations with the decimal numbers.}} (1 page)</ref>
<ref name="Kämmerer_1969">{{cite book |title=Digitale Automaten – Theorie, Struktur, Technik, Programmieren |language=de |chapter=I.12. Theorie: Minimierung Boolescher Funktionen |first=Wilhelm |last=Kämmerer |author-link=:de:Wilhelm Kämmerer |editor-first1=Hans |editor-last1=Frühauf |editor-link1=:de:Hans Frühauf |editor-first2=Wilhelm |editor-last2=Kämmerer |editor-first3=Kurz |editor-last3=Schröder |editor-first4=Helmut |editor-last4=Winkler |edition=1 |date=May 1969 |publisher=[[Akademie-Verlag GmbH]] |publication-place=Berlin, Germany |location=Jena, Germany |volume=5 |id=License no. 202-100/416/69. Order no. 4666 ES 20 K 3. |series=Elektronisches Rechnen und Regeln |pages=98, 103–104 |url=https://books.google.com/books?id=jkcgAQAAIAAJ&q=P.+W.+Abraham+I.+G.+Nordahl |quote-page=98 |quote=[...] 1955 wurde das Verfahren auf die bequemere dezimale Schreibweise umgestellt ({{citeref|Abrahams|Nordahl|1955|P. W. Abraham und I. G. Nordahl|style=plain}} in [<nowiki/>{{citeref|Caldwell|1958|Caldwell|style=plain}}<nowiki/>]). [...]}} (NB. A second edition 1973 exists as well.<!-- where the relevant quote is located on page 99 rather than 98 -->)</ref>
<ref name="McColl_1878">{{cite journal |first=Hugh |last=McColl |author-link=Hugh McColl (mathematician) |date=1878-11-14 |title=The Calculus of Equivalent Statements (Third Paper) |journal=[[Proceedings of the London Mathematical Society]] |volume=s1-10<!-- or 10? --> |issue=1 |doi=10.1112/plms/s1-10.1.16 |pages=16–28 |url=https://academic.oup.com/plms/article-abstract/s1-10/1/16/1503062|url-access=subscription }}</ref>
<ref name="Blake_1932">{{cite journal |first=Archie |last=Blake |title=Canonical expressions in Boolean algebra |series=Abstracts of Papers |journal=[[Bulletin of the American Mathematical Society]] |date=November 1932 |page=805}}</ref>
<ref name="Blake_1937">{{cite book |last=Blake |first=Archie |date=1938 |orig-date=1937 |title=Canonical Expressions in Boolean Algebra |type=Dissertation |publisher=[[University of Chicago Libraries]] |location=Chicago, Illinois, USA |edition=Lithographed |page=36 |url=https://books.google.com/books?id=gqRYAAAAMAAJ |quote-page=36 |quote=[...] this method was known to [[Charles Sanders Peirce|Peirce]] and his students [...] It is mentioned at several places in Studies in Logic, by members of the [[Johns Hopkins University]], 1883 [...]}} (ii+60 pages)</ref>
<ref name="Blake_1938">{{cite journal |first=Archie |last=Blake |title=Corrections to ''Canonical Expressions in Boolean Algebra'' |journal=[[The Journal of Symbolic Logic]] |issn=0022-4812 |publisher=[[Association for Symbolic Logic]] |volume=3 |issue=2 |date=June 1938 |doi=10.2307/2267595 |jstor=2267595 |url=https://projecteuclid.org/euclid.jsl/1183385465 |pages=112–113|s2cid=5810863 |url-access=subscription }}</ref>
<ref name="Samson_1954">{{cite book |last1=Samson |first1=Edward Walter |last2=Mills |first2=Burton E. |date=April 1954 |title=Circuit Minimization: Algebra and Algorithms for New Boolean Canonical Expressions |publisher=[[Air Force Cambridge Research Center]] |id=Technical Report AFCRC TR 54-21 |location=Bedford, Massachusetts, USA}}</ref>
<ref name="Nelson_1955">{{cite journal |last=Nelson |first=Raymond J. |date=June 1955 |title=Simplest Normal Truth Functions |journal=[[The Journal of Symbolic Logic]] |publisher=[[Association for Symbolic Logic]] |volume=20 |issue=2 |doi=10.2307/2266893 |jstor=2266893 |pages=105–108|s2cid=32920372 }} (4 pages)</ref>
<ref name="Ladd_1883">{{cite book |last=Ladd |first=Christine |author-link=Christine Ladd |date=1883 |chapter=On the algebra of logic |editor-first=Charles Sanders |editor-last=Peirce |editor-link=Charles Sanders Peirce |title=Studies in Logic |location=Boston, USA |publisher=[[Little, Brown & Company]] |pages=17–71 |quote-page=23 |quote=[...] If the reduction [of an expression to simplest form] is not evident, it may be facilitated by taking the negative of the expression, reducing it, and then restoring it to the positive form. [...]}}</ref>
<ref name="Fielder_1966">{{cite journal |title=Classroom Reduction of Boolean Functions |first=Daniel C. |last=Fielder |journal=[[IEEE Transactions on Education]] |publisher=[[IEEE]] |volume=9 |issue=4 |date=December 1966 |issn=0018-9359 |eissn=1557-9638 |doi=10.1109/TE.1966.4321989 |bibcode=1966ITEdu...9..202F |pages=202–205}}</ref>
<ref name="Brown_2010">{{cite journal |title=McColl and Minimization |journal=History and Philosophy of Logic |volume=31 |number=4 |pages=337–348 |publisher=[[Taylor & Francis]] |issn=1464-5149 |date=November 2010 |orig-date=2010-10-27 |doi=10.1080/01445340.2010.517387 |first=Frank Markham |last=Brown<!-- |author-link=Frank Markham Brown --> |s2cid=216590641 |url=https://www.researchgate.net/publication/233139704 |access-date=2020-04-15 |url-status=live |archive-url=https://web.archive.org/web/20200415201838/https://www.researchgate.net/publication/233139704_McColl_and_Minimization |archive-date=2020-04-15}}</ref>
<ref name="Majumder_2015">{{cite conference |title=Investigation on Quine McCluskey Method: A Decimal Manipulation Based Novel Approach for the Minimization of Boolean Function |first1=Alak |last1=Majumder |first2=Barnali |last2=Chowdhury |first3=Abir J. |last3=Mondal |first4=Kunj |last4=Jain |location=Department of Electronics & Communication, Engineering National Institute of Technology, Arunachal Pradesh Yupia, India |date=2015-01-30 |orig-date=2015-01-09 |type=Conference paper |conference=2015 International Conference on Electronic Design, Computer Networks & Automated Verification (EDCAV), Shillong, India  |doi=10.1109/EDCAV.2015.7060531 |pages=18–22 |url=https://www.researchgate.net/publication/301408055 |access-date=2020-05-08 |url-status=live |archive-url=https://web.archive.org/web/20200508200648/https://www.researchgate.net/publication/301408055_Investigation_on_Quine_McCluskey_method_A_decimal_manipulation_based_novel_approach_for_the_minimization_of_Boolean_function
 |archive-date=2020-05-08}} [https://www.researchgate.net/profile/Alak_Majumder2/publication/301408055_Investigation_on_Quine_McCluskey_method_A_decimal_manipulation_based_novel_approach_for_the_minimization_of_Boolean_function/links/5948a1bba6fdcc70635a3706/Investigation-on-Quine-McCluskey-method-A-decimal-manipulation-based-novel-approach-for-the-minimization-of-Boolean-function.pdf] (NB. This work does not cite the prior art on decimal methods.) (5 pages)</ref>
<ref name="Holdsworth_2002">{{cite book |title=Digital Logic Design |chapter=3.17 Decimal approach to Quine–McCluskey simplification of Boolean algebra |first1=Brian |last1=Holdsworth |first2=Clive |last2=Woods |edition=4 |date=2002 |publisher=[[Newnes Books]] / [[Elsevier Science]] |isbn=((0-7506-4588-2))<!-- this ISBN is faulty, but actually printed in the book --> |pages=65–67 |chapter-url=https://books.google.com/books?id=o7enSwSVvgYC&pg=PA65 |url=https://books.google.com/books?id=o7enSwSVvgYC |access-date=2020-04-19}} (519 pages) [https://web.archive.org/web/20200419213939/http://s2.bitdownload.ir/Ebook/Electronics/Holdsworth%20-%20Digital%20Logic%20Design%204e%20HQ%20(Newnes,%202002).pdf]</ref>
<ref name="ChandraMarkowsky_1978">{{cite journal |title=On the number of prime implicants |first1=Ashok K. |last1=Chandra  |first2=George |last2=Markowsky |journal=Discrete Mathematics |volume=24 |number=1 |date=1978 |pages=7–11 |doi=10.1016/0012-365X(78)90168-1 |doi-access=free }}</ref>
}}