Talk:Implicant

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I changed an implication sign to face the other way, unless it was supposed to be some other kind of symbol, someone check it please? —Comment added by 131.111.202.114 (talk) 21:00, 1 June 2009 (UTC)[reply]

Tried to make things clearer, I hope it didn't get worse :). --pietro 7 July 2005 13:18 (UTC)

Given the cleanup tag, I tried to make this clearer, but I may not have misunderstood it myself. When I first encountered it, the first paragraph was "In Boolean logic, an implicant of a given Boolean function F of n variables is a product term P such that for every combination of the n variables for which P takes the value 1, F is also equal to 1. Therefore P implies F." I did my best to make this slightly clearer, but I am completely unfamiliar with the phrase "product term", on which we do not have an article, so perhaps I have misunderstood. Also, I am not sure what it would mean for an implicant to be minimal. Does it mean that it could not be a function in fewer variables? Isn't it possible to have two distinct implicants neither of which is reducible? -- Jmabel | Talk 07:32, Nov 28, 2004 (UTC)

EDIT: "The sum of all prime implicants of a Boolean function is called its complete sum, minimal covering sum, or Blake canonical form."

The above is not true regarding minimal sums. The function F(abcd) = A(!B)(!C) + ABD + (!A)BC also includes A(!C)D and BCD as primes, but the minimal sum does not require these. To answer the questions posed above, it would not be correct to refer to an implicant as minimal. An implicant is *prime* if it contains no extra variables. So in the function F(ab) = AB + B, both terms are implicants but term AB is not prime since variable A is clearly redundant (easily proved: F = B(A + 1) = B(1) = B). Minimal sums only contain primes, but you have to be careful what you mean if you say `a minimal sum contains all primes` since the set of all primes of a function can be greater than those required for a minimal sum (functions may also have more than one minimal sum).97.65.103.250 (talk) 22:51, 25 February 2016 (UTC)C. Theriault[reply]

Cover ?[edit]

The terms cover, covering, .. are used many time and never defined. There is not even a link to its definition. One could hope to find it in https://en.wikipedia.org/wiki/Canonical_normal_form but here, the word cover is absent. Furthermore, cover is too vague to be easily searched, its a really common word.

Could someone correct this problem please ?Arthur MILCHIOR (talk) 02:26, 9 November 2017 (UTC)[reply]