Co-NP-complete - Co-NP-complete In complexity theory, the complexity class Co-NP-complete is the set of problems that are the hardest problems in Co-NP, in the sense that they are the ones most likely not to be in P. If you can find a way to solve a Co-NP-complete problem quickly, then you can use that algorithm to solve all Co-NP problems quickly. A more formal definition: A decision problem C is Co-NP-complete if it is in Co-NP and if every problem in Co-NP is many-one reducible to it. This means that for every Co-NP problem L, there exists a polynomial time algorithm which can transform any instance of L into an instance of C with the same truth value. As a consequence, if we had a polynomial time algorithm for.
NP-complete - NP-complete In complexity theory, the NP-complete problems are the hardest problems in NP, in the sense that they are the ones most likely not to be in P. The reason is that if you could find a way to solve an NP-complete problem quickly, then you could use that algorithm to solve all NP problems quickly. (A more formal definition is given below. See also Complexity classes P and NP). One example of an NP-complete problem is the subset sum problem which is: given a finite set of integers, determine whether any non-empty subset of them adds up to zero. A supposed answer is very easy to verify for correctness, but no-one knows a faster way to solve the problem than to try every single possible.
Isotope table (complete) - Isotope table (complete) This table shows all of the known isotopes of the chemical elements, arranged with increasing atomic number from left to right and increasing neutron number from top to bottom. Half lives are indicated by the color of each isotope's cell, with isotopes having alternative decay paths having differing foreground and background colors. For this same table divided into more manageable pieces, see Isotope table (divided). The data for this table came from http://www2.bnl.gov/CoN/nuchart1.html Half lives El Unstable El 1-10 days El 10-100 days El 100 days - 10 years El 10-10,000 years El >10,000 years El Natural radioactive El Stable Complete listing of known isotopes p 1 2 H He 3 4 n H Li Be 5 6 1 D 3He B C 7 2.
AI-complete - AI-complete AI-complete is a slang term (derived from NP-Complete) for a group of problems in computer science that seem to require a fundamental breakthrough in Artificial Intelligence research to solve. A problem is called AI-complete if it seems to be so difficult that any AI program solving that problem would also be smart enough to solve every other problem in AI. That is by analogy with an NP-complete problem, which is so difficult that any fast solution to it would let us quickly solve all other NP problems. The slang is usually used humorously, not literally. It reflects an attitude that these problems won't be solved by simple tricks, such as those used in ELIZA. Such problems include: Computer vision Natural language understanding Passing the Turing Test.
Complexity classes P and NP - Complexity classes P and NP Computational complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. The most common resources are time (how many steps does it take to solve a problem) and space (how much memory does it take to solve a problem). In this theory, the class P consists of all those decision problems that can be solved on a deterministic sequential machine in an amount of time that is polynomial in the size of the input; the class NP consists of all those decision problems whose positive solutions can be verified in polynomial time given the right information, or equivalently, whose solution can be found in polynomial time on a non-deterministic machine. The biggest.
Co-NP - Co-NP In complexity theory, co-NP is the complexity class that contains the complements of decision problems in the complexity class NP. The complement of a decision problem is here defined as the problem with the yes and no answers reversed, or if we define decision problems as sets of finite strings as the complement of this set with respect to the given alphabet. From this definition it follows that the complement of every decision problem in NP is in co-NP and the complement of every decision problem in co-NP is in NP. P is a subset of both NP and co-NP. That subset is thought to be strict in both cases. NP and co-NP are also thought to be unequal. If so, then no NP-complete problem can.
Completeness - mathematics and related technical fields, a mathematical object is complete if nothing needs to be added to it. This is made precise in various ways, several of which have a related notion of completion. Metric spaces or uniform spaces are said to be complete if every Cauchy sequence in them converges. See complete space. An ordered field is complete if every non-empty subset of it that has an upper bound within the field has a least upper bound within the field. Up to isomorphism there is only one complete ordered field: the field of real numbers. In functional analysis, a subset S of a topological vector space V is complete if its span is dense in V. If V is separable, it follows that any vector in V can be written.
P-complete - P-complete In complexity theory, the class P-complete is a set of decision problems and is useful in the analysis of which problems can be efficiently solved on parallel computers. A decision problem is in P-complete if it is in P, and every problem in P can be reduced to it in polylogarithmic time on a parallel computer with a polynomial number of processors. In other words, a problem A is in P-complete if, for each problem B in P, there are constants c and k such that B can be reduced to A in time O((log n)c) using O(nk) parallel processors. See NC for the definition of parallel processors. The class P, typically taken to consist of all the "tractable" problems for a sequential computer, contains.
PSPACE-complete - PSPACE-complete In complexity theory, PSPACE-complete is a set of decision problems. A problem is in PSPACE-complete if it is in PSPACE, and every problem in PSPACE can be reduced to it in polynomial time. The problems in PSPACE-complete can be thought of as the hardest problems in PSPACE. These problems are widely suspected to be outside of P and NP, but that is not known. It is known that they lie outside of NC. The first known NP-complete problem was satisfiability (SAT). This is the problem of whether there are assignments of truth values to variables that make a boolean expression true. For example, one instance of SAT would be the question of whether the following is true: The most basic PSPACE-complete problem is identical, except every.
NP (complexity) - NP (complexity) In computational complexity theory, NP ("non-deterministic polynomial-time") is the set of decision problems solvable in polynomial time on a non-deterministic Turing machine. Or, equivalently, YES answers are checkable in polynomial time on a deterministic Turing machine given the right information. A language L belongs to NP if there exists a two input polynomial time algorithm A and a constant c such that L = {x in {0,1}* ∃ certificate, y with y = O(xc) such that A(x,y) = 1} Algorithm A verifies L in polynomial time. See also: Complexity classes P and NP and NP-Complete..
NP-hard - NP-hard In computational complexity theory, NP-hard (Non-deterministic Polynomial-time hard) refers to the class of decision problems that contains all problems H such that for all decision problems L in NP there is a polynomial-time many-one reduction to H. Informally this class can be described as containing the decision problems that are at least as hard as any problem in NP. This intuition is supported by the fact that if we can find an algorithm A that solves one of these problems H in polynomial time then we can construct a polynomial time algorithm for every problem in NP by first executing the reduction from this problem to H and then executing the algorithm A. Assuming language L to be NP-complete, 1. L is in NP 2..
NP-equivalent - NP-equivalent In complexity theory, NP-equivalent is the set of problems that are both NP-easy and NP-hard. NP-equivalent is similar to NP-complete, except the problems in NP-equivalent do not have to be decision problems. For example, the problem FIND-SUBSET-SUM is in NP-equivalent. Given a set of integers, FIND-SUBSET-SUM is the problem of finding some subset of the integers that adds up to zero (or returning the empty set if there is no such subset). This optimization problem is similar to the decision problem SUBSET-SUM. Given a set of integers, SUBSET-SUM is the problem of finding whether there exists a subset summing to zero. SUBSET-SUM is NP-complete. To show that FIND-SUBSET-SUM is NP-equivalent, we must show that it is both NP-hard and NP-easy. Clearly it is NP-hard. If.
Knight's Tour - during the centuries: differently sized boards two-player games based on this idea problems using slight variations on the way the knight moves. The knight's tour problem is an instance of the more general hamiltonian path problem in graph theory, which is NP-complete. The problem of getting a closed knight's tour is similarly an instance of the hamiltonian cycle problem. See How to solve the knight's tour for instructions on solving the knight's tour problem. Note however that, unlike the general hamiltonian path problem, the knight's tour problem can be solved in linear time (Conrad et al 1994). The pattern made by a Knight's Tour has often been used as a literary constraint. The earliest instance of this is found in Rudrata's Kavyalankara written during the 9th century. In the 20th century.
Vertex cover problem - In computer science, the Vertex Cover Problem is an NP-complete problem in complexity theory. A vertex cover in a graph is a subset of the verticies of the graph, chosen with the property that one of the endpoints of each edge is in the subset. In the graph at right, {1,3,5,6} is an example of a vertex cover. The vertex cover problem is the optimization problem of finding a vertex cover of minimum size in a graph. The problem is a decision problem, so we wonder if a vertex cover of size k exists in the graph. VERTEX COVER = { k <= the number of vertices in G, G is a graph with a clique of size k or less} A brute force algorithm to find a vertex cover.
Internet slang - yourself". The use of this acronym is ambigious and not recommended. GG --- "good going" or "good game". Used sincerely in online games such as trivia, but more often used sarcastically when someone has done something foolish. Also, it is now becoming customary for all players to say "gg" when the game is over in such games as Counter-Strike, unless a player is profoundly displeased with the outcome. GJ --- "good job" h8 --- "hate"; or h1 to h9 to indicate how much does a person hates something. Example: "h9 brocoli." HAND --- "have a nice day" HTH --- "hope this helps" IANAL --- "I am not a lawyer". Usually used before a non-lawyer gives legal advice, as a humorous disclaimer. IANARS --- "I am not a rocket scientist" IC ---.
Integer factorization - would be 32·5. The factorization is always unique, according to the fundamental theorem of arithmetic. This problem is of significance in mathematics, cryptography, complexity theory, and quantum computers. The complete list of factors can be derived from the prime factorization by incrementing the exponents from zero until the number is reached. For example, since 45 = 32·5, 45 is divisible by 30·50, 30·51, 31·50, 31·51, 32·50, and 32·51, or 1, 5, 3, 15, 9, and 45. In contrast, the prime factorization only includes prime factors. Given two large prime numbers, it is easy to multiply them together. However, given their product, it appears to be difficult to find the factors. This is relevant for many modern systems in cryptography. If a fast method were found for solving the integer factorization problem,.
Independent Set problem - Set problem The Independent Set (IS) problem is an NP-complete problem. Description An independent set is defined as a subset of a vertices in a graph that are not connected together. Input: A graph G An integer K Question: Does G have an independent set of at least size K? Proof of Independent Set being NP-complete (Reduce from 3-CNF-SAT a version of the Boolean satisfiability problem) 1. Certificate: Check that no vertices are connecting. Can easily be verified in polynomial time. 2. 3-CNF-SAT->IS transformation 3-CNF-SAT (Given): Variables x1, x2, ..., xn Clauses c1, c2, ..., cm IS (Construction of Graph): 1 vertex for each occurrence of each literal (3m vertices) Connect two vertices when: They are conflicting (i.e. x1, ~x1) They are in the same clause This transformation can be performed.
Isotope table (divided) - cell, with isotopes having alternative decay paths having differing foreground and background colors. The whole table can be found in one piece at Isotope table (complete). The data for these tables came from http://www2.bnl.gov/CoN/nuchart1.html Table of contents showTocToggle("show","hide") 1 Legend 2 Isotopes for elements 1-15 3 Isotopes for elements 16-30 4 Isotopes for elements 31-45 5 Isotopes for elements 46-60 6 Isotopes for elements 61-75 7 Isotopes for elements 76-90 8 Isotopes for elements 91-105 9 Isotopes for elements 106-111 Legend Half lives El Unstable El 1-10 days El 10-100 days El 100 days - 10 years El 10-10,000 years El >10,000 years El Natural radioactive El Stable Isotopes for elements 1-15 p 1 2 H He 3 4 n H Li Be 5 6 1 D 3He B C 7.
ISO 3166-1 - country or territory generally gets new alpha codes if its name changes, whereas a new numeric code is associated with a change of boundaries. Some codes in each series are reserved, for various reasons. ISO 3166-1 is not the only standard for country codes. The following is intended to be a complete ISO 3166-1 code list in alphabetical order by country name (encoding list). 004 AFG AF (ISO 3166-2) Afghanistan 008 ALB AL (ISO 3166-2) Albania 012 DZA DZ (ISO 3166-2) Algeria 016 ASM AS (ISO 3166-2) American Samoa 020 AND AD (ISO 3166-2) Andorra 024 AGO AO (ISO 3166-2) Angola 660 AIA AI (ISO 3166-2) Anguilla 010 ATA AQ (ISO 3166-2) Antarctica 028 ATG AG (ISO 3166-2) Antigua and Barbuda 032 ARG AR (ISO 3166-2) Argentina 051 ARM AM (ISO.
ISO 3166-1 alpha-2 - are tracked by ISO 3166-3. Note that AA, ZZ and the ranges QM-QZ and XA-XZ are reserved for private use. In addition, OO is designated as an escape code. If a country code cannot be found in the list then it is probably obsolete, in which case it should be found in the list of obsolete country codes, further below. The following is intended to be a complete list of current ISO 3166-1 two-letter codes. AD - Andorra AE - United Arab Emirates AF - Afghanistan AG - Antigua and Barbuda AI - Anguilla (AI previously represented French Afars and Issas) AL - Albania AM - Armenia AN - Netherlands Antilles AO - Angola AQ - Antarctica (defined here as everything south of latitude 60°S) AR - Argentina AS - American.
