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Class of problems in computer science
In complexity theory, PP, or PPT is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability
PP_(complexity)
Topics referred to by the same term
secreted by PP cells PP cell or pancreatic polypeptide cell pro parte, abbreviated p.p., for a type of synonymy in taxonomy PP (complexity), a probabilistic
PP
Estimate of time taken for running an algorithm
the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly
Time_complexity
Feature of systems that defy description
Complexity characterizes the behavior of a system or model whose components interact in multiple ways and follow local rules, leading to non-linearity
Complexity
Measure of the structural complexity of a software program
Cyclomatic complexity is a software metric used to indicate the complexity of a program. It is a quantitative measure of the number of linearly independent
Cyclomatic_complexity
Inherent difficulty of computational problems
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource
Computational complexity theory
Computational_complexity_theory
Amount of resources to perform an algorithm
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus
Computational_complexity
Class of problems solvable in polynomial time
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class. It contains all decision problems that can
P_(complexity)
Algorithmic runtime requirements for common math procedures
the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity of performing computations
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Measure of algorithmic complexity
theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer
Kolmogorov_complexity
Computer memory needed by an algorithm
The space complexity of an algorithm or a data structure is the amount of memory space required to solve an instance of the computational problem as a
Space_complexity
Notion in combinatorial game theory
Combinatorial game theory measures game complexity in several ways: State-space complexity (the number of legal game positions from the initial position)
Game_complexity
Computational complexity of quantum algorithms
Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational
Quantum_complexity_theory
Measure of complexity of real-valued functions
learning theory (machine learning and theory of computation), Rademacher complexity, named after Hans Rademacher, measures richness of a class of sets with
Rademacher_complexity
Concept in computer science
In computational complexity theory, a branch of computer science, bounded-error probabilistic polynomial time (BPP) is the class of decision problems solvable
BPP_(complexity)
Complexity class (logarithmic space)
In computational complexity theory, L (also known as LSPACE, LOGSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved
L_(complexity)
Complexity of sending information in a distributed algorithm
In theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem
Communication_complexity
Concept in linguistics
Language complexity is a topic in linguistics which can be divided into several sub-topics such as phonological, morphological, syntactic, and semantic
Language_complexity
1977 scholarly article by Donald Knuth
"The Complexity of Songs" is a scholarly article by computer scientist Donald Knuth published in 1977 as an in-joke about computational complexity theory
The_Complexity_of_Songs
Application of complexity science to economics
Complexity economics, or economic complexity, is the application of complexity science to the problems of economics. It relaxes several common assumptions
Complexity_economics
The polynomial hierarchy is contained in probabilistic Turing machine in polynomial time
Toda's theorem is a result in computational complexity theory that was proven by Seinosuke Toda in his paper "PP is as Hard as the Polynomial-Time Hierarchy"
Toda's_theorem
Complexity class used to classify decision problems
problems in computer science In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems
NP_(complexity)
Complexity class
science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass
PPAD_(complexity)
Branch of computational complexity theory
In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according
Parameterized_complexity
Set of problems in computational complexity theory
In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly
Complexity_class
Concept in psychology
Cognitive complexity describes cognition along a simplicity-complexity axis. It is the subject of academic study in fields including personal construct
Cognitive_complexity
Argument by proponents of intelligent design
Irreducible complexity (IC) is the argument that certain biological systems with multiple interacting parts would not function if one of the parts were
Irreducible_complexity
Field in logic and theoretical computer science
science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational
Proof_complexity
Discrete Fourier transform algorithm
of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O ( n 2 ) {\textstyle O(n^{2})} , which arises
Fast_Fourier_transform
Model of computational complexity
In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according
Circuit_complexity
Computational complexity class of problems
In computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial
BQP
Concept in computer science
In complexity theory, ZPP (zero-error probabilistic polynomial time) is the complexity class of problems for which a probabilistic Turing machine exists
ZPP_(complexity)
In computational complexity theory, the complement of a decision problem is the decision problem resulting from reversing the yes and no answers. Equivalently
Complement_(complexity)
Randomized polynomial time class of computational complexity theory
In computational complexity theory, randomized polynomial time (RP) is the complexity class of decision problems for which a probabilistic Turing machine
RP_(complexity)
Creating sequence of numbers that cannot be predicted
multiple years. Flipism League of entropy List of random number generators PP (complexity) Procedural generation Random password generator Random variable, contains
Random_number_generation
Computational complexity class
In computational complexity theory, the complexity class E is the set of decision problems that can be solved by a deterministic Turing machine in time
E_(complexity)
Class in computational complexity theory
}{=}}{\mathsf {P}}} More unsolved problems in computer science In computational complexity theory, the class NC (for "Nick's Class") is the set of decision problems
NC_(complexity)
Complexity class
computational complexity theory, the class QIP (which stands for Quantum Interactive Proof) is the quantum computing analogue of the classical complexity class
QIP_(complexity)
Complexity class
In computational complexity theory, the complexity class FNP is the function problem extension of the decision problem class NP. The name is somewhat
FNP_(complexity)
computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather
Structural_complexity_theory
System composed of many interacting components
and Complexity", exploring the diversity of problem types by contrasting problems of simplicity, disorganized complexity, and organized complexity. Weaver
Complex_system
In computational complexity theory, SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t
SL_(complexity)
Framework for scoring a behavior's complexity
The model of hierarchical complexity (MHC) is a framework for scoring how complex a behavior is, such as verbal reasoning or other cognitive tasks. It
Model of hierarchical complexity
Model_of_hierarchical_complexity
String that certifies the answer to a computation
In computational complexity theory, a certificate (also called a witness) is a string that certifies the answer to a computation, or certifies the membership
Certificate_(complexity)
Attribute of machine learning models
The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function
Sample_complexity
complexity class contained in PP defined via GapP functions. The class often arises in the context of quantum computing. AWPP contains the complexity
AWPP
Unsolved problem in computer science
World Sci. Publ., Hackensack, NJ. pp. 3319–3336. MR 3966534. Lance Fortnow. Computational Complexity Blog: Complexity Class of the Week: Factoring. 13
P_versus_NP_problem
is estimating stationary distribution for an ergodic Markov chain. The complexity class is not known to equal PL, and an attempt to simulate PL through
PL_(complexity)
Number and type of nodes and alternative paths that exist within a computer network
"Quantitative Measures of Network Complexity". Complexity in Chemistry, Biology, and Ecology. Boston, MA: Springer. pp. 191–235. doi:10.1007/0-387-25871-X_5
Network_complexity
In computational complexity theory, a language B (or a complexity class B) is said to be low for a complexity class A (with some reasonable relativized
Low_(complexity)
Notion of the "hardest" or "most general" problem in a complexity class
In computational complexity theory, a computational problem is complete for a complexity class if it is, in a technical sense, among the "hardest" (or
Complete_(complexity)
Concept in computational complexity theory
In computational complexity theory, BPL (Bounded-error Probabilistic Logarithmic-space), sometimes called BPLP (Bounded-error Probabilistic Logarithmic-space
BPL_(complexity)
Computational complexity
in computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that
NL_(complexity)
Algorithm characteristic in computations
In computational complexity theory, the average-case complexity of an algorithm is the amount of some computational resource (typically time) used by the
Average-case_complexity
Complexity class
In computational complexity theory, SC (Steve's Class, named after Stephen Cook) is the complexity class of problems solvable by a deterministic Turing
SC_(complexity)
Russian submachine gun
method of operation; an unlocked breech system reduces cost and build complexity. The Bizon's operating cycle is characterized by a very short recoil stroke;
PP-19_Bizon
Branch of mathematical logic
Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic
Descriptive_complexity_theory
State complexity is an area of theoretical computer science dealing with the size of abstract automata, such as different kinds of finite automata. The
State_complexity
Complexity class
In computational complexity theory, the complexity class FP is the set of function problems that can be solved by a deterministic Turing machine in polynomial
FP_(complexity)
Measure of complexity regarding algorithmic entropy
theory, sophistication is a measure of complexity related to algorithmic entropy. When K is the Kolmogorov complexity and c is a constant, the sophistication
Sophistication (complexity theory)
Sophistication_(complexity_theory)
Function that counts distinct factors of a string
In computer science, the complexity function of a word or string (a finite or infinite sequence of symbols from some alphabet) is the function that counts
Complexity_function
Creationist argument by William Dembski
Specified complexity is a creationist intelligent design argument introduced by William Dembski. According to Dembski, the concept can formalize a property
Specified_complexity
Complexity class
In computational complexity theory, Polynomial Local Search (PLS) is a complexity class that models the difficulty of finding a locally optimal solution
PLS_(complexity)
Algorithm that employs a degree of randomness as part of its logic or procedure
Papadimitriou (1993), Computational Complexity (1st ed.), Addison Wesley, ISBN 978-0-201-53082-7 Chapter 11: Randomized computation, pp. 241–278. Rabin, Michael
Randomized_algorithm
Complexity class
In computational complexity theory, PostBQP is a complexity class consisting of all of the computational problems solvable in polynomial time on a quantum
PostBQP
science, and specifically computational complexity theory and circuit complexity, TC (Threshold Circuit) is a complexity class of decision problems that can
TC_(complexity)
(Randomized Logarithmic-space Polynomial-time), is the complexity class of computational complexity theory problems solvable in logarithmic space and polynomial
RL_(complexity)
Axioms in computational complexity theory
In computational complexity theory the Blum axioms or Blum complexity axioms are axioms that specify desirable properties of complexity measures on the
Blum_axioms
Concept in computational complexity
In complexity theory, the counting hierarchy is a hierarchy of complexity classes. It is analogous to the polynomial hierarchy, but with NP replaced with
Counting_hierarchy
Type of computational problem
In computational complexity theory and computability theory, a counting problem is a type of computational problem that is obtained by strengthening a
Counting_problem_(complexity)
In computational complexity theory, the complexity class FL is the set of function problems that can be solved by a deterministic Turing machine in a
FL_(complexity)
Complexity class
In computational complexity theory, PPA is a complexity class, standing for "Polynomial Parity Argument" (on a graph). Introduced by Christos Papadimitriou
PPA_(complexity)
Algorithmic runtime requirements for matrix multiplication
in computer science In theoretical computer science, the computational complexity of matrix multiplication dictates how quickly the operation of matrix
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Collection of loosely coupled services used to build computer applications
modularity, scalability, and adaptability. However, it introduces additional complexity, particularly in managing distributed systems and inter-service communication
Microservices
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
Type of computer science algorithm
that space complexity also has varied choices in whether or not to count the index lengths as part of the space used. Often, the space complexity is given
In-place_algorithm
In convex geometry and polyhedral combinatorics, the extension complexity of a convex polytope P {\displaystyle P} is the smallest number of facets among
Extension_complexity
Concept in topology
In mathematics, topological complexity of a topological space X (also denoted by TC(X)) is a topological invariant closely connected to the motion planning
Topological_complexity
Numerical measure of program structure
better known for introducing cyclomatic complexity. McCabe defined essential complexity as the cyclomatic complexity of the reduced CFG (control-flow graph)
Essential_complexity
American computer scientist (born 1981)
University of Texas at Austin. His primary areas of research are computational complexity theory and quantum computing. Aaronson grew up in the United States, though
Scott_Aaronson
ACC, is a class of computational models and problems defined in circuit complexity, a field of theoretical computer science. The class is defined by augmenting
ACC0
Rules out assigning to arbitrary functions their computational complexity
computational complexity theory, Blum's speedup theorem, first stated by Manuel Blum in 1967, is a fundamental theorem about the complexity of computable
Blum's_speedup_theorem
Concept of art that can be described by a computer program
Low-complexity art was described by Jürgen Schmidhuber in 1997, defined as art that can be described by a short computer program (that is, a computer program
Low-complexity_art
Measure in information theory
Logical depth is a measure of complexity for individual strings devised by Charles H. Bennett based on the computational complexity of an algorithm that can
Logical_depth
Determining the answers to a query on a database
database. Research in database theory aims at determining the computational complexity of answering different kinds of queries over databases, in particular
Query_evaluation
Complexity class from interactive proofs
In computational complexity theory, the class IP (which stands for interactive proof) is the class of problems solvable by an interactive proof system
IP_(complexity)
Interactive proof system in computational complexity theory
In computational complexity theory, an Arthur–Merlin protocol, introduced by Babai (1985), is an interactive proof system in which the verifier's coin
Arthur–Merlin_protocol
Upper bound on resources required by an algorithm
In computer science (specifically computational complexity theory), the worst-case complexity measures the resources (e.g. running time, memory) that
Worst-case_complexity
Approach to the study of finite semigroups and automata
between finite automata and semigroups. Decidability of Krohn-Rhodes complexity long motivated much work in semigroup theory. In June 2024, Stuart Margolis
Krohn–Rhodes_theory
Algorithm analysis method
theoretical computer science, smoothed analysis is a way of measuring the complexity of an algorithm. Since its introduction in 2001, smoothed analysis has
Smoothed_analysis
Calculations of the game complexity of go
Go). Generalized Go is played on n × n boards, and the computational complexity of determining the winner in a given position of generalized Go depends
Go_and_mathematics
Data structure for storing non-overlapping sets
cell probe complexity of dynamic data structures". Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89. pp. 345–354.
Disjoint-set_data_structure
Algorithmic complexity class
In computational complexity theory, the complexity class EXPTIME (sometimes called EXP or DEXPTIME) is the set of all decision problems that are solvable
EXPTIME
Unsolved problem in computational complexity theory
time nor to be NP-complete, and therefore may be in the computational complexity class NP-intermediate. It is known that the graph isomorphism problem
Graph_isomorphism_problem
theoretical computer science, multiparty communication complexity is the study of communication complexity in the setting where there are more than two players
Multiparty communication complexity
Multiparty_communication_complexity
Class of computational complexity
}{=}}PSPACE}}} More unsolved problems in computer science In computational complexity theory, PSPACE is the set of all decision problems that can be solved
PSPACE
Self-balancing binary search tree
Additionally, after finding a node for insertion and deletion, the amortized complexity of the tree restructuring operations is constant. Adding or deleting the
WAVL_tree
2011 book by Robert Axelrod
The Complexity of Cooperation, by Robert Axelrod, is the sequel to The Evolution of Cooperation. It is a compendium of seven articles that previously appeared
The_Complexity_of_Cooperation
Standard model in theoretical computer science
In computational complexity theory, arithmetic circuits are the standard model for computing polynomials. Informally, an arithmetic circuit takes as inputs
Arithmetic_circuit_complexity
Complexity class of bounded-depth circuits
AC0 (alternating circuit) is a complexity class used in circuit complexity. It is the smallest class in the AC hierarchy, and consists of all families
AC0
PP COMPLEXITY
PP COMPLEXITY
Surname or Lastname
English
English : of uncertain origin; perhaps from Middle English atte knappe (from Old English cnæpp ‘hill’ or ‘summit’), a topographic name for someone who lived at the top of a hill.
Surname or Lastname
German
German : occupational name or status name from the German word Knapp(e), a variant of Knabe ‘young unmarried man’. In the 15th century this spelling acquired the separate, specialized meanings ‘servant’, ‘apprentice’, or ‘miner’.German : in Franconia, a nickname for a dexterous or skillful person.English : topographic name for someone who lived by a hillock, Middle English knappe, Old English cnæpp, or habitational name from any of the several minor places named with the word, in particular Knapp in Hampshire and Knepp in Sussex.German and western Slavic : variant of Knabe.
PP COMPLEXITY
PP COMPLEXITY
Female
French
Pet form of French Michèle, MICHELINE means "who is like God?"
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Vishnu
Girl/Female
African, American, Arabic, Danish, Gujarati, Hindu, Indian, Kannada, Latin, Sanskrit, Tamil
Blessing of God; Origin; Popularity; Variants
Boy/Male
Indian, Sanskrit
Virtuous Path
Boy/Male
Indian, Telugu
Moon
Boy/Male
Finnish Hebrew
Girl/Female
English
Dark-skinned.
Female
African
Monday-born.
Girl/Female
Norse
Wife of Sigmund.
Boy/Male
Latin
He who loves God. Famous Bearer: late composer Wolfgang Amadeus Mozart.
PP COMPLEXITY
PP COMPLEXITY
PP COMPLEXITY
PP COMPLEXITY
PP COMPLEXITY
n.
The state of being complex; intricacy; entanglement.
n.
The state or quality of being intricate or entangled; perplexity; involution; complication; complexity; that which is intricate or involved; as, the intricacy of a knot; the intricacy of accounts; the intricacy of a cause in controversy; the intricacy of a plot.
a.
Of or pertaining to katabolism; as, katabolic processes, which give rise to substances (katastates) of decreasing complexity and increasing stability.
n.
The state of being complex; complexity.
n.
Complexity.
a.
Very soft; -- a direction to execute a passage as softly as possible. (Abbrev. pp.)
n.
The act or process of complicating; the state of being complicated; intricate or confused relation of parts; entanglement; complexity.
n.
A rearrangement or concentration of the different constituents of one or more substances into a distinct and definite compound of greater complexity and molecular weight, often resulting in an increase of density, as the condensation of oxygen into ozone, or of acetone into mesitylene.
imp. & pp.
of Classify
n.
An assemblage of parts or organs, either in animal or plant, essential to the performance of some particular function or functions which as a rule are of greater complexity than those manifested by a single organ; as, the capillary system, the muscular system, the digestive system, etc.; hence, the whole body as a functional unity.
n.
That which is complex; intricacy; complication.
pl.
of Complexity
n.
The state of being complex; complexity.