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Topic: Disjunctive normal form

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	PlanetMath: DNF
		A propositional formula is a DNF formula, meaning Disjunctive Normal Form, if it is a disjunction of conjunctions of literals (a literal is a propositional variable or its negation).
		This is version 1 of DNF, born on 2004-03-09.
		Object id is 5677, canonical name is DNF.
	planetmath.org /encyclopedia/DisjunctiveNormalForm.html (75 words)

	Disjunctive normal form
		Disjunctive Normal Form or DNF is a method of standardizing and normalizing logical formulas.
		A logical formula is considered to be in DNF if and only if it is a single disjunction of conjunctions.
		More simply stated, the outermost operators of the formula are all ORs, and there is only one level of nesting allowed, which may only contain literals[?] or conjunctions of literals.
	www.ebroadcast.com.au /lookup/encyclopedia/dn/DNF.html (184 words)

	Andrews. To Truth through Proof.
		Negation normal form is defined, and the two-dimensional representation is introduced (conjuncts=vertical paths and disjuncts=horizontal paths).
		System F of first-order logic is introduced in the usual way (with disjunction, negation, and universal quantification as primitive)--except he allows propositional, function and relation variables over which we cannot quantify.
		The system F is modified to include existential quantifiers as primitive and called system E. A wff G in E is in prenex normal form iff no vacuous quantifier occurs and no quantifier occurs in the scope of a propositional connective.
	gtps.math.cmu.edu /cebrown/notes/tttp.html (6301 words)

	Normal forms (Site not responding. Last check: 2007-11-03)
		The disjunctive normal form is used by default.
		Alternatively a conjunctive normal form can be selected as simplification target, which is a form with leading operator and.
		Internally the full normal forms are computed as intermediate result; in these forms each term contains all leaf expressions, each one exactly once.
	www.uni-koeln.de /REDUCE/boolean/node3.html (196 words)

	Resolution Method. Normal Forms. Skolem. Mathematical Logic. Part 5.
		Note that a formula and its Skolem normal form are not equivalent (even in the classical logic!), they are only a kind of "semi-equivalent": a set of formulas is inconsistent, iff so is the set of their Skolem normal forms.
		Let us continue the "normalization" process that we started in Section 5.1 by reducing formulas to their prenex normal forms, where all quantifiers are gathered in front of a formula that does not contain quantifiers.
		Since, in general, Skolem normal form is not equivalent to the initial formula, we cannot use reduction to Skolem normal forms in the usual ("positive", or affirmative) proofs.
	linas.org /mirrors/www.ltn.lv/2005.01.29/~podnieks/mlog/ml5.htm (5338 words)

	Unification with Disjunctive Descriptions
		DNF expansion of a description is however an expensive task -- the process takes exponential time in the worst case (Kasper and Rounds, 1986).
		Reducing the disjunctiveness of the description: By reducing the extent of the description, we reduce the amount of disjunction to be expanded, and thus speed up the expansion process.
		Using some form of structure sharing in the expansion process: in the expansion process, the same terms may be multiplied together a number of times.
	www.wagsoft.com /PapersHtml/IWPT93/node2.html (757 words)

	CogSci 108b: Knowledge Representation and Logic
		And this expression is in disjunctive normal form.
		Form a conjunction from the combinations found in 2, by using the positive literal for truth values of 1, and the negated literal for truth values of 0.
		Computing the conjunctive normal form of a predicate logic expression can be done directly, but a useful algorithm involves starting with a DNF.
	cogsci.ucsd.edu /~batali/108b/lectures/logic.html (5038 words)

	Selected papers
		Embora a transformação para a forma normal conjuntiva e sua posterior simplificação seja um assunto bastante estudado, devido à sua aplicação ao método de prova automática por resolução, a transformação dual, para a forma normal disjuntiva, principalmente para o caso da lógica de primeira ordem, não mereceu a mesma atenção.
		Although the transformation into conjunctive normal form, and its further simplification, has been extensively studied, because of its application in the resolution method for automatic theorem proving, the dual transformation, into disjunctive normal form, has not deserved the same atention, mainly in the first-order case.
		In this paper, we present some results that show that, unlikely the conjunctive norma form, the disjunctive normal form is not unique for the first-order case, and that the determination of its minimal form presents several suptilities.
	www.das.ufsc.br /~gb/lista-publi.html (1272 words)

	Propositional Logic (Site not responding. Last check: 2007-11-03)
		We are often given a Boolean function in truth table form and must derive a corresponding logical expression.
		Conjunctive and disjunctive normal forms are duals of each other; either one may be used to generate a logical expression from a truth table.
		With these normal forms, we can be more precise about how to generate a logical expression from a truth table.
	www.cs.rochester.edu /u/leblanc/csc173/proplogic/expressions.html (1815 words)

	Minimizing Boolean Functions
		In this form, the function is written as the logical OR (indicated by +) of a set of AND terms, one per minterm.
		There is also a conjunctive normal form, which represents an expression as a product of sums rather than as a sum of products.
		A prime implicant is a product term that will generate ones only for combinations of inputs that are minterms of the disjunctive normal form of the function, and which cannot be further reduced by combining with any other term.
	babbage.cs.qc.edu /courses/Minimize/index.php (3640 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Converts a term already in negation normal form into disjunctive normal form.
		When applied to a term already in negation normal form (see NNF_CONV), meaning that all other propositional connectives have been eliminated in favour of disjunction, disjunction and negation, and negation is only applied to atomic formulas, WEAK_DNF_CONV puts the term into an equivalent disjunctive normal form, which is a disjunction of conjunctions.
		The ordering and associativity of the resulting form are not guaranteed, and it may contain duplicates.
	www.cl.cam.ac.uk /~jrh13/hol-light/HTML/WEAK_DNF_CONV.html (148 words)

	redlog User Manual - Groebner Simplifier
		The functions differ in the boolean normal form that is computed at the beginning.
		After computing the corresponding normal form, the formula is simplified using Groebner simplification techniques.
		If this switch is on then conjunctions of inequalities and disjunctions of equations are contracted multiplicatively to one atomic formula.
	www.fmi.uni-passau.de /~redlog/htmldoc/redlog_29.html (592 words)

	INTERACTIVE WEB PAGE (Site not responding. Last check: 2007-11-03)
		Sat := To check if a given formula is satisfiable using it's pretty DNF form.
		Displays the normal form such that only the disjunctive clause of a CNF and the conjunctive clauses of a
		DNF are delineated by brackets and no other subformulas.
	www.cse.iitd.ernet.in /~csu02127/INT5.html (330 words)

	CSCI546+646: 15
		It seems as though being able to determine the disjunctive normal form for a boolean function would trivially solve the SAT problem.
		Since the disjunctive normal form lists the truth assignments and so solves SAT we can be sure that any mapping to disjunctive normal form will NOT take polynomial time.
		Notice that reducing to disjunctive normal form is not a problem in the technical sense so we can't say that it is NP-complete.
	www.csci.csusb.edu /dick/cs546/15.html (1880 words)

	Novell Documentation: Volera Excelerator XL 1.0 - Understanding Access Control Policies
		To facilitate the evaluation of rules, Excelerator XL 1.0 uses disjunctive normal form (DNF) and conjunctive normal form (CNF) to define the relationships between the conditions and sets within a given rule.
		The first rule shown in Figure 18 is in disjunctive normal form, meaning that the conditions within the rule are joined by And and the two sets are joined by Or.
		The second rule shown in Figure 18 would be in disjunctive normal form if it contained multiple sets, because the sets would be joined with either And or And Not.
	www.novell.com /documentation/ex10lnx/21ex3_dg/data/akm9df1.html (1984 words)

	Applications
		Recall that a proposition is in conjunctive normal form (C
		is a disjunction of propositional variables or their negations.
		is quite easy, by using the definition of validity and the properties ensured by the normalization procedure to show the two forms agree on all assignments.
	www.cs.uwyo.edu /~jlc/prop_gloss/node25.html (251 words)

	Math Forum - Ask Dr. Math Archives: College Logic/Set Theory (Site not responding. Last check: 2007-11-03)
		An interesting logic puzzle about determining a birthday leads to a discussion about interpretation, logic, and seeming confusion when one of the logic statements is rewritten in a different but equivalent form.
		Let A be the set of all sequences of the form (d1, d2, 23,...) where di = 0 or 1 and there are only a finite number of 1's in the sequence.
		The set Q of all rational numbers and the set N2 of all ordered pairs of natural numbers are countable.
	mathforum.org /library/drmath/sets/college_logic.html (950 words)

	Computer Science - CS 340 Discrete Structures for Engineers (4 credits) (Site not responding. Last check: 2007-11-03)
		Use elementary counting techniques to count simple finite structures that are either ordered or unordered and to count the worst case number of comparisons for simple decision trees.
		Apply the properties of propositional calculus to: determine whether a wff is a tautology, a contradiction, or a contingency; construct equivalence proofs; and transform truth functions and wffs into conjunctive normal form and disjunctive normal form.
		Apply the properties of first-order predicate calculus to: determine whether a wff is valid, invalid, satisfiable, or unsatisfiable; construct equivalence proofs; and transform first-order wffs into prenex conjunctive or disjunctive normal form.
	www.cs.pdx.edu /course.php?cid=371 (468 words)

	On Information Factoring in Dublin Metadata Records (Site not responding. Last check: 2007-11-03)
		The semantics of repeated fields and groups (and, equivalently, of references to other metadata records) are described using sentential logic, and a proposal is made to specify the interpretation of repeating groups using the disjunctive normal form of corresponding logical expressions.
		A human may easily realize that the first form (TEI Lite) applies only to the first identifier, and that the second and third identifiers are for objects in the second form (HTML); software will realize it only if suitably instructed.
		Note, in passing, that from the elements we can infer that the first instantiation is not identical to the second or third, but the second and third instantiations, both being in HTML, could conceivably be identical.
	www.ifla.org /documents/libraries/cataloging/metadata/dublin3.htm (3086 words)

	[No title]
		Explain and show how to use a truth table in order to construct a conjunctive normal form for any Boolean formula W. Hint: Consider the disjunctive normal form for (W. The exclusive-or operator (, is defined by the rule that a (b is true whenever a or b is true but not both.
		Prove or disprove that x+ (y (z) = (x+ y) ((x+ z) Prove or disprove that x ((y + z) = (x (y) + (x (z) Write conjunctive normal form and disjunctive normal form formulae for x (y The exclusive-or operator is not complete.
		Which one(s), if any, of the three operators {and, or, not} can be combined with exclusive-or to make a complete set.
	www.stonehill.edu /compsci/Discrete-Math-II/asg1.doc (991 words)

	Propositional Logic (Site not responding. Last check: 2007-11-03)
		To construct a logical expression in conjunctive normal form from a truth table:
		These laws state that the negation of the conjunction (or disjunction) of two propositions is logically equivalent to the disjunction (or conjunction) of their negations.
		We cannot use propositional logic to establish the truth of a proposition that isn't given as a premise, or which can't be inferred by the laws of inference.
	www.cs.rochester.edu /u/leblanc/csc173.94/proplogic.html (3769 words)

	Related Work (Site not responding. Last check: 2007-11-03)
		His method for quantified variable elimination always introduces disjunctions, even if the result is convex.
		However, I believe that the Omega test will prove better for quantified variable elimination when the result is convex and better for verification of a formula already in disjunctive normal form.
		Cooper's algorithm does not require formulas to be transformed into disjunctive normal form and may be better for formulas that would be expensive to put into disjunctive normal form (although our methods for handling negation address this as well).
	www.cs.umd.edu /projects/omega/subsectionstar3_2_1.html (375 words)

	Disjunctive Normal Form from FOLDOC (Site not responding. Last check: 2007-11-03)
		(DNF) A logical formula consisting of a disjunction of conjunctions where no conjunction contains a disjunction.
		the DNF of (A or B) and C is (A and C) or (B and C).
		Nearby terms: discussion group « Disiple « disjoint union « Disjunctive Normal Form » disk » disk controller » disk drive
	ftp.sunet.se /foldoc/foldoc.cgi?DNF (53 words)

	Boolean Expression Manipulation -- from Mathematica Information Center
		The package will produce truth tables, evaluate tautologies, and test for equivalence.
		It will also return the Boolean expression in either Disjunctive Normal Form or Conjunctive Normal Form using the DNF and CNF functions.
		Applied Mathematics, Boolean algebra, boolean expressions, boolean logic, true, false, truth table, truthtable, tautology, tautologyq, disjunctive normal form, conjunctive normal form
	library.wolfram.com /infocenter/MathSource/4187 (83 words)

	Maggie Johnson
		CNF: A sentence that is a conjunction of one or more disjunctions of one or more literals.
		DNF: A sentence that is a disjunction of one or more conjunctions of one or more literals.
		Can a sentence be in both CNF and DNF?
	cse.stanford.edu /classes/cs103a/h7Consequence.html (667 words)

	Class pdkb.Clause
		A clause is a disjunction (#$or) of literals.
		Return t if the argument, a Conjunctive Normal Form (CNF), represents a Ground Atomic Formulan (GAF).
		Construct a new Clause from the argument, a Conjunctive Normal Form formula.
	ai.uga.edu /~bancroft/pub/pdkb/doc/pdkb.Clause.html (839 words)

	Lecture 20 - integer programming
		36.4-5 Give a polynomial-time algorithm to satisfy Boolean formulas in disjunctive normal form.
		The DNF formula can become exponentially large and hence the reduction cannot be done in polynomial time.
		We must transform every instance of a known NP-complete problem to an instance of the problem we are interested in.
	www.cs.sunysb.edu /~algorith/lectures-good/node20.html (565 words)

	BoolView - boolean function analyzer (Site not responding. Last check: 2007-11-03)
		The list of problems involved consists of but not limited to the following items:
		Obtaining algebraic normal form (also known as ring sum expansion, Zhegalkin's polynom)
		Future releases will support some other problems concerning circuits and cryptography.
	www.maxolute.com (292 words)

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