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I have also reverted the change from -(A v B) to -(A & B); IMO, since A v B is more obvious to be in CNF than A&B (even if the second still is), then it's clear that the negation (rather than the binary connective) is the problem there. I have also added an explanation for A&B to be in
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A formula in CNF is a conjunction of clauses. There is in general no obligation for a clause to contain all variables, which is a special case. Can you provide a source for the statement that every clause must contain all variables? Clearly, in some cases this is necessary, but is not part of the
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I have been studying boolean algebra in my class "Fundamentals of Logic Design", and we are taught that CNF is more than just product of sums. We are taught that every sum (clause) must contain every literal. *This* is what makes the form useful for comparing functions and performing automatic
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is, in the definitions I am used to, both in CNF and DNF. It is in CNF because it is the conjunction of two disjunctions of literals (the disjunctions being 'A' and 'B'). It is in DNF because it is the disjunction of a conjunction of literals (there is only one disjunct, and it is
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Bah. Conjunctive normal form is not a method. There is a method to construct a conjunctive normal form of a logical function, but the CNF, the result of this method is not the method. A method is not the same as the result of this. Be exact, please :-)) (a mathematician).
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Shouldn't the complexity of converting a formula into CNF, preserving validity, be coNP-hard? Because the validity problem for a DNF is coNP-hard and it can be decided by converting the DNF into CNF (the validity of a CNF can be decided in linear time)?
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Conjunctive normal form and clausal normal form are indeed the same thing. See, for example, Melvin
Fitting, First order logic and automated theorem proving, second edition, page 28. Thus I vote to merge
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These transformations are based on creating new variables that represent the truth value of a subformula (should the fact that new variables are necessary be mentioned in the article?). For example,
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Shouldn't it be "distribute ORs over ANDs"? Where i am interpreting "distribute ANDs over ORs" to mean the act of converting things like "A AND (B OR C)" into things like "(A AND B) OR (A AND C)".
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If 4-SAT is defined like 3-SAT (all clauses have at most 4 literals), the problem is NP-complete, like any other k-SAT problem with k: -->
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I am curious as to the source of this statement. I am particularly interested in reading what these transformations are specifically. --
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2. The recent edit stating that 4-SAT is linear is incorrect unless a different definition of 4-SAT is considered. Source? -
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Knowledge. If you would like to participate, please visit the project page, where you can join
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In circuit design it seems common to use a different definition than the one used in logic:
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analysis. Please comment, i'm interested to know how this is formally defined and used.
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I think it can be merged, over various internet sources both are treated same..
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An illuminating question to ask in your logic class would be - if
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The method of converting a formula into a CNF is not introduced.
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I'm not quite sure, but in my Logic class I've been told that
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Optimality of a Fast CNF Conversion and its Use with SAT
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