33 relations: Alternating Turing machine, Cambridge University Press, Closed timelike curve, Complement (complexity), Complement (set theory), Computational complexity theory, Context-sensitive language, Decision problem, Descriptive complexity theory, DSPACE, EXPSPACE, EXPTIME, Interactive proof system, IP (complexity), Kleene star, NL (complexity), Non-deterministic Turing machine, Nondeterministic algorithm, NP (complexity), P (complexity), PH (complexity), Polynomial, Polynomial-time reduction, PSPACE-complete, QIP (complexity), Quantum computing, Savitch's theorem, Second-order logic, Space hierarchy theorem, Transitive closure, True quantified Boolean formula, Turing machine, Union (set theory).
In computational complexity theory, an alternating Turing machine (ATM) is a non-deterministic Turing machine (NTM) with a rule for accepting computations that generalizes the rules used in the definition of the complexity classes NP and co-NP.
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.
The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.
Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.
Christmas traditions vary from country to country.
In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime that is "closed", returning to its starting point.
In computational complexity theory, the complement of a decision problem is the decision problem resulting from reversing the yes and no answers.
In set theory, the complement of a set refers to elements not in.
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
In formal language theory, a context-sensitive language is a language that can be defined by a context-sensitive grammar (and equivalently by a noncontracting grammar).
In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.
Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic needed to express the languages in them.
In computational complexity theory, DSPACE or SPACE is the computational resource describing the resource of memory space for a deterministic Turing machine.
In complexity theory, '' is the set of all decision problems solvable by a deterministic Turing machine in O(2p(n)) space, where p(n) is a polynomial function of n. (Some authors restrict p(n) to be a linear function, but most authors instead call the resulting class.) If we use a nondeterministic machine instead, we get the class, which is equal to by Savitch's theorem.
In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that have exponential runtime, i.e., that are solvable by a deterministic Turing machine in O(2p(n)) time, where p(n) is a polynomial function of n. In terms of DTIME, We know and also, by the time hierarchy theorem and the space hierarchy theorem, that so at least one of the first three inclusions and at least one of the last three inclusions must be proper, but it is not known which ones are.
In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two parties.
In computational complexity theory, the class IP (which stands for Interactive Polynomial time) is the class of problems solvable by an interactive proof system.
In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters.
In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems which can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space.
New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.
New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.
In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.
In theoretical computer science, a Turing machine is a theoretical machine that is used in thought experiments to examine the abilities and limitations of computers.
In computer science, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm.
In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.
In computational complexity theory, the complexity class PH is the union of all complexity classes in the polynomial hierarchy: PH was first defined by Larry Stockmeyer.
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
In computational complexity theory, a polynomial-time reduction is a method of solving one problem by means of a hypothetical subroutine for solving a different problem (that is, a reduction), that uses polynomial time excluding the time within the subroutine.
In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (polynomial space) and if every other problem that can be solved in polynomial space can be transformed to it in polynomial time.
In computational complexity theory, the class QIP, which stands for Quantum Interactive Polynomial time, is the quantum computing analogue of the classical complexity class IP, which is the set of problems solvable by an interactive proof system with a polynomial-time verifier and one computationally unbounded prover.
Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.
In computational complexity theory, Savitch's theorem, proved by Walter Savitch in 1970, gives a relationship between deterministic and non-deterministic space complexity.
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic.
In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines can solve more problems in (asymptotically) more space, subject to certain conditions.
In mathematics, the transitive closure of a binary relation R on a set X is the smallest relation on X that contains R and is transitive.
In computational complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas.
A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules.
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.
2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.