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Topic: Boolean function

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	Springer Online Reference Works
		Boolean functions are one of the main subjects of discrete mathematics, in particular, of mathematical logic and mathematical cybernetics.
		Boolean functions first occurred in the mathematical formulation of logical problems, and were named after G.
		Boolean functions, metric theory of), as well as of the various algebras of Boolean functions (cf.
	eom.springer.de /b/b016940.htm (656 words)

	Boolean Algebra Revisited - Page 1
		Boolean algebra is described as a finite algebra due to the finite number of values that are represented in the algebra.
		A Boolean expression consisting of variables and operators is known as a Boolean function.
		The symbols used for the operators in Boolean functions and formulas are: a dot (or frequently an and) for the AND operator.
	users.senet.com.au /~dwsmith/boolean.htm (4017 words)

	Boolean function - Wikipedia, the free encyclopedia
		In mathematics, a finitary boolean function is a function of the form f : B
		More generally, a function of the form f : X → B, where X is an arbitrary set, is a boolean-valued function.
		The properties of boolean functions play a critical role in cryptography, particularly in the design of symmetric key algorithms (see S-box).
	en.wikipedia.org /wiki/Boolean_function (239 words)

	XML Path Language (XPath)
		A FunctionCall expression is evaluated by using the FunctionName to identify a function in the expression evaluation context function library, evaluating each of the Arguments, converting each argument to the type required by the function, and finally calling the function, passing it the converted arguments.
		Each function in the function library is specified using a function prototype, which gives the return type, the name of the function, and the type of the arguments.
		NOTE: The number function should not be used for conversion of numeric data occurring in an element in an XML document unless the element is of a type that represents numeric data in a language-neutral format (which would typically be transformed into a language-specific format for presentation to a user).
	www.w3.org /TR/xpath (8473 words)

	Generating the Monotone Boolean Functions
		An elementary way of constructing and counting these functions is to begin with a function of n=0 variables, which can only have a constant state, either 0 or 1, with no logical operations at all.
		In general a Boolean function of n variables consists of the specification of the output state (either 0 or 1) for each of the 2^n possible input states.
		Each of these functions can be represented by a 2^n bit binary number F in the range from 0 to 2^(2^n) - 1, and each input state can be represented by an n-bit number I in the range from 0 to 2^n - 1.
	www.mathpages.com /home/kmath094.htm (484 words)

	boolean
		Boolean function is a function whose domain is a set of n-tuples of 0's and 1's, and whose range is an element of the basic Boolean set {0,1}.
		For example, the minterm expansion for a Boolean function f of three variables might be represented as follows (taking the values directly from the truth table):
		A Karnaugh map is a 2-dim representation of the truth table for a Boolean function.
	cse.stanford.edu /classes/cs103a/h9BAlgebra.htm (2594 words)

	Active Boolean Function Nonlinearity Measurement in JavaScript (Site not responding. Last check: 2007-08-16)
		But it is convenient to pair the functions which are the same except for the value of the constant, and then we have exactly 8 affine Boolean functions of 3 variables.
		Another way to compute Boolean correlation is to accumulate the bits of one function (as integers) by addition or subtraction as selected by the other function.
		Nonlinearity is the number of bits which must change in the truth table of a Boolean function to reach the closest affine function.
	www.ciphersbyritter.com /JAVASCRP/NONLMEAS.HTM (2482 words)

	BBC - h2g2 - Boolean Function Reduction
		It shows that Boolean functions having three or more arguments may be expressed as a composition of functions having only two arguments, including a method for achieving this simplification.
		A general Boolean function has a number of arguments, and a unique value depending only upon those arguments - with the arguments and function value being limited to one of two distinct values, which we shall call true and false.
		We have shown that a function F of n arguments can be expressed as a composition of functions of two arguments, and the sub-functions P and Q, which have n-1 arguments only.
	www.bbc.co.uk /dna/h2g2/A2266760 (781 words)

	Boolean Functions
		A Boolean function is an expression formed with binary variables and logical operators, e.g.
		In essence a truth table is a list which defines a Boolean function.
		Boolean Algebra: A mathematical system for formulating logical statements with symbols so that problems can be solved in a manner to ordinary algebra.
	scitec.uwichill.edu.bb /cmp/online/P10F/boolean.htm (268 words)

	Database of Boolean Functions
		All equivalence classes of Boolean functions of up to 6 variables with respect to A, B, C, and D are available from [1].
		Number of equivalence classes of Boolean functions with respect to symmetries A, B, C, and D. (These numbers are also found as sequence A001289 in the On-Line Encyclopedia of Integer Sequences.)
		The number of equivalence classes of Boolean functions with 6 variables and degree less than or equal to 3 is 851,520.
	www.ii.uib.no /~larsed/boolean (397 words)

	Boolean Logic
		(A boolean function is just one in which all the inputs are boolean values, and the output is a boolean value.) Sum-of-products is a method you can use create these gate systems.
		The output of the OR gate is the output of the function.
		For practice, you can try implementing some of the other basic boolean functions, such as NOR (true when both inputs are 0, false otherwise) and NAND (false when both inputs are 1, true otherwise).
	www.cs.princeton.edu /~lworthin/126/precepts/boolean.html (1942 words)

	Measured Boolean Function Nonlinearity in Feistel Cipher Constructions (Site not responding. Last check: 2007-08-16)
		Nonlinearity is the number of bits which must change in the truth table of a Boolean function to reach the closest affine function, and thus is a measure of one kind of cipher strength.
		The nonlinearity of a Boolean function is the Hamming distance to the closest affine function [e.g., PIE88, PIE89, PIE89B].
		Each result value is essentially a correlation count to a particular affine function, and the minimum distance (the maximum correlation) is found by scanning the transform results.
	www.ciphersbyritter.com /ARTS/FEISNONL.HTM (714 words)

	3.5 Simplification of Boolean Functions
		Since there are an infinite variety of boolean functions of n variables, but only a finite number of unique boolean functions of those n variables, you might wonder if there is some method that will simplify a given boolean function to produce the optimal form.
		Assuming your boolean function is in canonical form (sum of minterms), insert ones for each of the truth map entries corresponding to a minterm in the function.
		An important thing you must keep in mind when optimizing boolean functions using the mapping method is that you always want to pick the largest rectangles whose sides' lengths are a power of two.
	webster.cs.ucr.edu /AoA/Linux/HTML/DigitalDesign3.html (1840 words)

	Boolean Function Simplification (Site not responding. Last check: 2007-08-16)
		In some cases the simplified Boolean expressions are not unique.
		For the case when there is not a unique answer the number of terms and the number of variables they contain should be identical, but the terms themselves may be different.
		Karnaugh input: The variable names (again single letters) are input in a window to determine their names and how many variables there are.
	hopper.unco.edu /KARNAUGH1.1/Function.html (560 words)

	Minimizing Boolean Functions
		There are many rules for manipulating a boolean expression algebraically, but there is just one rule that you need in order to minimize a function once it is in disjunctive normal form, the rule of complementation.
		Some functions have "don't care" conditions, which are combinations of inputs that will never occur, resulting in cases where it doesn't matter whether the output is a zero or a one.
		For our sample function, minterms 2, 3, and 4 are each covered by exactly one prime implicant, so all three of the prime implicants are essential, there is just one minimized form, and there is nothing more to do.
	babbage.cs.qc.edu /courses/Minimize/index.php (3640 words)

	Boolean function
		Unlike the Boolean class constructor, the Boolean() function does not use the keyword new.
		Moreover, the Boolean class constructor initializes a Boolean object to false if no parameter is specified, while the Boolean() function returns undefined if no parameter is specified.
		Boolean values are compared by value, and Boolean objects are compared by reference.
	www.adobe.com /livedocs/flashlite/2/main/00000149.html (320 words)

	Boolean - Wikipedia, the free encyclopedia
		A Boolean value is a truth value, either 'true' or 'false', often coded 1 and 0, respectively.
		A Boolean-valued function of one variable is a characteristic function or an indicator function of a subset of its domain, namely "the support" of that function
		In computer science, "Boolean" is a datatype, usually a primitive datatype.
	en.wikipedia.org /wiki/Boolean (180 words)

	Boolean Valued Function (Site not responding. Last check: 2007-08-16)
		One nice advantage to the boolean type is to create functions that return true or false.
		The details of the complicated test will be hidden inside the function, and the function call will add clarity to the program.
		This is much clearer than putting the details of the boolean test in the main program.
	www.cs.fiu.edu /~downeyt/cop2210/boolean.html (240 words)

	Boolean Function Complexity - Cambridge University Press (Site not responding. Last check: 2007-08-16)
		Boolean function complexity, the combinatorial study of such networks, is a subject that started back in the 1950s and has today become one of the most challenging and vigorous areas of theoretical computer science.
		The range of topics covered will be of interest to the newcomer to the field as well as the expert, and overall the papers are representative of the research presented at the Symposium.
		Anyone with an interest in Boolean Function complexity will find that this book is a necessary purchase.
	www.cambridge.org /catalogue/catalogue.asp?isbn=0521408261 (198 words)

	Boolean (Flex™ 2 Language Reference)
		Use the Boolean class to retrieve the primitive data type or string representation of a Boolean object.
		To create a Boolean object, you can use the constructor or the global function, or assign a literal value.
		A reference to the class object or constructor function for a given object instance.
	livedocs.macromedia.com /flex/2/langref/Boolean.html (388 words)

	Graph-Based Algorithms for Boolean Function Manipulation - Bryant (ResearchIndex) (via CobWeb/3.1 planetlab1.tamu.edu) (Site not responding. Last check: 2007-08-16)
		Abstract: In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms.
		Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on the ordering of decision variables in the graph.
		Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical...
	citeseer.ist.psu.edu.cob-web.org:8888 /bryant86graphbased.html (509 words)

	Method and apparatus for multi-function, stored logic Boolean function generation (US4120043)
		A stored logic Boolean function generator having a control word storage coupled to a control block for selectively configuring the control block into logic circuits for simulating either a logical AND circuit or a logical OR circuit for operating on binary signals.
		The results of the logical manipulation are stored in the other of the externally addressable stores which thus serves as a destination storage device.
		The binary data is continually circulated through the control block until the sequence of logical operations stored in the control word storage has been completed and the predetermined logical function performed.
	www.delphion.com /details?pn10=US04120043 (434 words)

	Lua Boolean function return problem - Indigo Rose Software Forums
		My attempts to build a function that returns a boolean value have failed.
		If I quote "true" and "false" the function works but I get a string value and not a boolean value back.
		The problem was not in the function but in my attempt to use its return value in Dialog.Message.
	www.indigorose.com /forums/showthread.php?p=53737 (320 words)

	boolean function (Site not responding. Last check: 2007-08-16)
		Definition: A function whose range is {0, 1}.
		See also binary function, predicate, boolean, boolean expression.
		Sandeep Kumar Shukla, "boolean function", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/booleanfnctn.html (90 words)

	BOOLEAN String Function
		The function will automatically scan for () pairs, adding the necessary) at the end of the search string or (at the beginning if required.
		INC DI precedes the MOV CL,[ES:DI] causing the function to consider the first character of Src_str to represent the length rather than the actual length byte.
		The function returns the offset from the beginning of the string, NOT the offset from Strt_at.
	atlas.csd.net /~cgadd/knowbase/STRINGS0060.HTM (790 words)

	boolean (Site not responding. Last check: 2007-08-16)
		Note: A mathematical boolean algebra based on a set of size n has 2
		Binary logic is the boolean algebra which two values.
		Paul E. Black, "boolean", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/boolean.html (156 words)

	Boolean Functions Simplification (Logic Minimization) (via CobWeb/3.1 planetlab1.tamu.edu) (Site not responding. Last check: 2007-08-16)
		A simple 5 input/5 output example is available to show the different ways of using the bfunc simplifiers...
		bfunc is a package for constructing or simplifying Boolean Functions from binary Truth (State) Tables, generating several kinds of output, from Truth Tables to Symbolic Equations, Binary Decision Trees, etc.
		A third possibility is to generate a Binary Decision Tree, which is converted to standard Sum of Products (this conversion step also reduces the number of literals, and, in some special cases, the number of logical products).
	www.dei.isep.ipp.pt.cob-web.org:8888 /~acc/bfunc (1340 words)

	Analysis of Boolean Functions
		The course is given by Guy Kindler, and will cover topics concerning analysis of Boolean functions, and their relations to computer science.
		The space of Boolean functions, the Fourier-Walsh representation, and some formulas connecting them.
		Testing whether a given Boolean function is a J-junta, in time polynomial in J. Learning Juntas.
	dimacs.rutgers.edu /~gkindler/boolean-course (161 words)

	[No title]
		This section describes the Boolean functions that you can call in a query.
		The XPath processor performs a Boolean comparison if either operand is a Boolean value.
		function on one operand to convert it to a Boolean value.
	www.stylusstudio.com /docs/v60/d_xpath44.html (425 words)

	XML Path Language (XPath): Booleans
		An object of type boolean can have one of two values, true and false.
		Numbers are compared for equality according to IEEE 754 IEEE754.
		Two booleans are equal if either both are true or both are false.
	www.stylusstudio.com /w3c/xpath/booleans.htm (709 words)

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