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Boyer–Moore Majority Vote Algorithm
The Boyer–Moore majority vote algorithm is an algorithm for finding the majority of a sequence of elements using linear time and a constant number of words of memory. It is named after Robert S. Boyer and J Strother Moore, who published it in 1981,. Originally published as a technical report in 1981. and is a prototypical example of a streaming algorithm. In its simplest form, the algorithm finds a majority element, if there is one: that is, an element that occurs repeatedly for more than half of the elements of the input. A version of the algorithm that makes a second pass through the data can be used to verify that the element found in the first pass really is a majority. If a second pass is not performed and there is no majority, the algorithm will not detect that no majority exists. In the case that no strict majority exists, the returned element can be arbitrary; it is not guaranteed to be the element that occurs most often (the mode of the sequence). It is not possible fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Word
In computing, a word is any Central processing unit, processor design's natural unit of data. A word is a fixed-sized Data (computing), datum handled as a unit by the instruction set or the hardware of the processor. The number of bits or digits in a word (the ''word size'', ''word width'', or ''word length'') is an important characteristic of any specific processor design or computer architecture. The size of a word is reflected in many aspects of a computer's structure and operation; the majority of the processor register, registers in a processor are usually word-sized and the largest datum that can be transferred to and from the computer memory, working memory in a single operation is a word in many (not all) architectures. The largest possible Memory address, address size, used to designate a location in memory, is typically a hardware word (here, "hardware word" means the full-sized natural word of the processor, as opposed to any other definition used). Documentation for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Misra–Gries Heavy Hitters Algorithm
Misra and Gries defined the ''heavy-hitters problem'' (though they did not introduce the term ''heavy-hitters'') and described the first algorithm for it in the paper ''Finding repeated elements''. Their algorithm extends the Boyer-Moore majority finding algorithm in a significant way. One version of the heavy-hitters problem is as follows: Given is a bag of elements and an integer . Find the values that occur more than times in . The Misra-Gries algorithm solves the problem by making two passes over the values in , while storing at most values from and their number of occurrences during the course of the algorithm. Misra-Gries is one of the earliest streaming algorithms, and it is described below in those terms in section #Summaries. Misra–Gries algorithm A bag is like a set in which the same value may occur multiple times. Assume that a bag is available as an array of elements. In the abstract description of the algorithm, we treat and its segments also as bags. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cellular Automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling. A cellular automaton consists of a regular grid of ''cells'', each in one of a finite number of ''State (computer science), states'', such as ''on'' and ''off'' (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its ''neighborhood'' is defined relative to the specified cell. An initial state (time ''t'' = 0) is selected by assigning a state for each cell. A new ''generation'' is created (advancing ''t'' by 1), according to some fixed ''rule'' (generally, a mathematical function) that dete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majority Problem (cellular Automaton)
The majority problem, or density classification task, is the problem of finding one-dimensional cellular automaton rules that accurately perform majority function, majority voting. Using local transition rules, cells cannot know the total count of all the ones in system. In order to count the number of ones (or, by symmetry, the number of zeros), the system requires a logarithmic number of bits in the total size of the system. It also requires the system send messages over a distance linear in the size of the system and for the system to recognize a non-regular language. Thus, this problem is an important test case in measuring the computational power of cellular automaton systems. Problem statement Given a configuration of a two-state cellular automaton with ''i'' + ''j'' cells total, ''i'' of which are in the zero state and ''j'' of which are in the one state, a correct solution to the voting problem must eventually set all cells to zero if ''i'' > ''j'' and must ev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Value
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as , disjunction (''or'') denoted as , and negation (''not'') denoted as . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his '' An Investigation of the Laws of Thought'' (1854). According to Huntington, the term ''Boolean algebra'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majority Function
In Boolean logic, the majority function (also called the median operator) is the Boolean function that evaluates to false when half or more arguments are false and true otherwise, i.e. the value of the function equals the value of the majority of the inputs. Boolean circuits A ''majority gate'' is a logical gate used in circuit complexity and other applications of Boolean circuits. A majority gate returns true if and only if more than 50% of its inputs are true. For instance, in a full adder, the carry output is found by applying a majority function to the three inputs, although frequently this part of the adder is broken down into several simpler logical gates. Many systems have triple modular redundancy; they use the majority function for majority logic decoding to implement error correction. A major result in circuit complexity asserts that the majority function cannot be computed by AC0 circuits of subexponential size. Properties For any ''x'', ''y'', and ''z'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Element Distinctness Problem
In computational complexity theory, the element distinctness problem or element uniqueness problem is the problem of determining whether all the elements of a list are distinct. It is a well studied problem in many different models of computation. The problem may be solved by sorting the list and then checking if there are any consecutive equal elements; it may also be solved in linear expected time by a randomized algorithm that inserts each item into a hash table and compares only those elements that are placed in the same hash table cell. Several lower bounds in computational complexity are proved by reducing the element distinctness problem to the problem in question, i.e., by demonstrating that the solution of the element uniqueness problem may be quickly found after solving the problem in question. Decision tree complexity The number of comparisons needed to solve the problem of size n, in a comparison-based model of computation such as a decision tree or algebraic decision t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loop Invariant
In computer science, a loop invariant is a property of a program loop that is true before (and after) each iteration. It is a logical assertion, sometimes checked with a code assertion. Knowing its invariant(s) is essential in understanding the effect of a loop. In formal program verification, particularly the Floyd-Hoare approach, loop invariants are expressed by formal predicate logic and used to prove properties of loops and by extension algorithms that employ loops (usually correctness properties). The loop invariants will be true on entry into a loop and following each iteration, so that on exit from the loop both the loop invariants and the loop termination condition can be guaranteed. From a programming methodology viewpoint, the loop invariant can be viewed as a more abstract specification of the loop, which characterizes the deeper purpose of the loop beyond the details of this implementation. A survey article covers fundamental algorithms from many areas of compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Logarithm
In mathematics, the binary logarithm () is the exponentiation, power to which the number must be exponentiation, raised to obtain the value . That is, for any real number , :x=\log_2 n \quad\Longleftrightarrow\quad 2^x=n. For example, the binary logarithm of is , the binary logarithm of is , the binary logarithm of is , and the binary logarithm of is . The binary logarithm is the logarithm to the base and is the inverse function of the power of two function. There are several alternatives to the notation for the binary logarithm; see the #Notation, Notation section below. Historically, the first application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ. Binary logarithms can be used to calculate the length of the representation of a number in the binary numeral system, or the number of bits needed to encode a message in infor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete mathematics, discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the Alphabet (formal languages), alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write, which direction to move the head, and whet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit Complexity
The bit is the most basic unit of information in computing and digital communication. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as either , but other representations such as ''true''/''false'', ''yes''/''no'', ''on''/''off'', or ''+''/''−'' are also widely used. The relation between these values and the physical states of the underlying storage or device is a matter of convention, and different assignments may be used even within the same device or program. It may be physically implemented with a two-state device. A contiguous group of binary digits is commonly called a '' bit string'', a bit vector, or a single-dimensional (or multi-dimensional) ''bit array''. A group of eight bits is called one ''byte'', but historically the size of the byte is not strictly defined. Frequently, half, full, double and quadruple words consist of a number of bytes which is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
