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Type of computational problem
in general, the counting problem corresponding to a decision problem X is called #X, where # is the number sign. Counting complexity techniques have significant
Counting_problem_(complexity)
Topics referred to by the same term
Counting problem may refer to: Enumeration Combinatorial enumeration Counting problem (complexity) This disambiguation page lists articles associated
Counting_problem
Finding the number of elements of a finite set
(bridge) Cardinal number Combinatorics Count data Counting (music) Counting problem (complexity) Counting sheep Counting-out game Developmental psychology
Counting
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
Problem of finding the best feasible solution
decision problems, the problem is more naturally characterized as an optimization problem. Counting problem (complexity) – Type of computational problem Design
Optimization_problem
Type of computational problem
In computational complexity theory, a function problem is a computational problem where a single output is expected for every input, but the output is
Function_problem
Inherent difficulty of computational problems
computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores
Computational complexity theory
Computational_complexity_theory
Yes/no problem in computer science
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a
Decision_problem
Problem a computer might be able to solve
prime factor of n. A counting problem asks for the number of solutions to a given search problem. For example, a counting problem associated with factoring
Computational_problem
Quantum algorithm for counting solutions to search problems
The Quantum counting algorithm is a quantum algorithm for efficiently counting the number of solutions for a given search problem. The algorithm is based
Quantum_counting_algorithm
Unsolved problem in computer science
seminal paper "The complexity of theorem proving procedures", and independently by Leonid Levin in 1973. Although the P versus NP problem was formally defined
P_versus_NP_problem
Class of computational problems
In computational complexity theory and computability theory, a search problem is a computational problem of finding an admissible answer for a given input
Search_problem
Problem of determining if a Boolean formula could be made true
integer k. #SAT, the problem of counting how many variable assignments satisfy a formula, is a counting problem, not a decision problem, and is #P-complete
Boolean satisfiability problem
Boolean_satisfiability_problem
Amount of resources to perform an algorithm
requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly
Computational_complexity
Unsolved problem in computational complexity theory
therefore may be in the computational complexity class NP-intermediate. It is known that the graph isomorphism problem is in the low hierarchy of class NP
Graph_isomorphism_problem
Type of computational problem
Computational problem Decision problem Optimization problem Search problem Counting problem (complexity) Function problem TFNP "Promise problem". Complexity Zoo
Promise_problem
Computational complexity of quantum algorithms
hardness of computational problems in relation to these complexity classes, as well as the relationship between quantum complexity classes and classical (i
Quantum_complexity_theory
Complexity class
meaning that every other problem in #P has a polynomial-time Turing reduction or polynomial-time counting reduction to it. A counting reduction is a pair of
♯P-complete
Problem that is difficult or impossible to solve
to solve one aspect of a wicked problem may reveal or create other problems. Due to their complexity, wicked problems are often characterized by organized
Wicked_problem
NP-hard problem in combinatorial optimization
In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances
Travelling_salesman_problem
Feature of systems that defy description
computational complexity are the time complexity of a problem equal to the number of steps that it takes to solve an instance of the problem as a function
Complexity
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)
Class in computational complexity theory
computer science In computational complexity theory, the class NC (for "Nick's Class") is the set of decision problems decidable in polylogarithmic time
NC_(complexity)
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
Set of objects whose state must satisfy limits
common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics
Constraint satisfaction problem
Constraint_satisfaction_problem
Complexity class
computational complexity theory, the complexity class #P (pronounced "sharp P" or, sometimes "number P" or "hash P") is the set of the counting problems associated
♯P
Type of computer science algorithm
ignoring their length. In this article, we refer to total space complexity (DSPACE), counting pointer lengths. Therefore, the space requirements here have
In-place_algorithm
Measure of algorithmic complexity
theorem, and Turing's halting problem. In particular, no program P computing a lower bound for each text's Kolmogorov complexity can return a value essentially
Kolmogorov_complexity
science, the Sharp Satisfiability Problem (sometimes called Sharp-SAT, #SAT or model counting) is the problem of counting the number of interpretations that
♯SAT
Decision problem in computer science
practice. SSP is a special case of the knapsack problem and of the multiple subset sum problem. The time complexity of SSP depends on two parameters: n - the
Subset_sum_problem
Sorting algorithm
Bucket sort may be used in lieu of counting sort, and entails a similar time analysis. However, compared to counting sort, bucket sort requires linked
Counting_sort
Determining the answers to a query on a database
computational complexity of answering different kinds of queries over databases, in particular over relational databases. The query evaluation problem takes two
Query_evaluation
(Randomized Logarithmic-space Polynomial-time), is the complexity class of computational complexity theory problems solvable in logarithmic space and polynomial
RL_(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
Task of computing complete subgraphs
& Trojanowski (1977), an early work on the worst-case complexity of the maximum clique problem. Also in the 1970s, beginning with the work of Cook (1971)
Clique_problem
Problem in computer science
In computational complexity theory and quantum computing, Simon's problem is a computational problem that is proven to be solved exponentially faster
Simon's_problem
Standard model in theoretical computer science
interesting open problem in computational complexity theory is the P vs. NP problem. Roughly, this problem is to determine whether a given problem can be solved
Arithmetic_circuit_complexity
of complexity classes in computational complexity theory. For other computational and complexity subjects, see list of computability and complexity topics
List_of_complexity_classes
Problem in combinatorial optimization
P≠NP, the O ( n W ) {\displaystyle O(nW)} complexity does not contradict the fact that the knapsack problem is NP-complete, since W {\displaystyle W}
Knapsack_problem
Problem transformation for counting solutions
computational complexity theory of counting problems, a polynomial-time counting reduction is a type of reduction (a transformation from one problem to another)
Polynomial-time counting reduction
Polynomial-time_counting_reduction
Problem in computer science
Unsolved problem in computer science What is the Turing run-time complexity of the square-root sum problem? More unsolved problems in computer science
Square-root_sum_problem
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)
Mathematical problem in operations research
optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible
Cutting_stock_problem
Problem of finding a cycle through all vertices of a graph
The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G
Hamiltonian_path_problem
Problem in theoretical computer science
conjecture on the query complexity of monotone graph properties, Gröger (1992) showed that any subgraph isomorphism problem has query complexity Ω(n3/2); that is
Subgraph_isomorphism_problem
Process of achieving a goal by overcoming obstacles
(1991). "Some comments on the study of complexity". In Sternberg, R. J.; Frensch, P. A. (eds.). Complex problem solving: Principles and mechanisms. Hillsdale
Problem_solving
The polynomial hierarchy is contained in probabilistic Turing machine in polynomial time
deterministic polynomial-time Turing reduction to a counting problem. An analogous result in the complexity theory over the reals (in the sense of Blum–Shub–Smale
Toda's_theorem
Complexity class
Yannakakis introduced the complexity class PLS in their paper "How easy is local search?". It contains local search problems for which the local optimality
PLS_(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
Computer science award
ISSN 0004-5411. Bulatov, Andrei A. (2013). "The complexity of the counting constraint satisfaction problem". Journal of the ACM. 60 (5). Association for
Gödel_Prize
Probability of shared birthdays
the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding
Birthday_problem
Software resource tracking technique
with this issue exist but can also increase the overhead and complexity of reference counting — on the other hand, these methods need only be applied to
Reference_counting
When a finite set S of relations yields polynomial-time or NP-complete problems
problems when the relations of S are used to constrain some of the propositional variables. It is called a dichotomy theorem because the complexity of
Schaefer's_dichotomy_theorem
Problem in computational complexity theory
>0} ? More unsolved problems in computer science In computational complexity theory, the online matrix-vector multiplication problem (OMv) asks an online
Online matrix-vector multiplication problem
Online_matrix-vector_multiplication_problem
Problem in computer science
Kolmogorov complexity P versus NP problem Termination analysis Worst-case execution time Calude, Cristian S. (2021). "Incompleteness and the Halting Problem".
Halting_problem
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
Algorithm that arranges lists in order
beginning of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its
Sorting_algorithm
Type of approximation algorithm
QPTAS has time complexity npolylog(n) for each fixed ε > 0. Furthermore, a PTAS can run in FPT time for some parameterization of the problem, which leads
Polynomial-time approximation scheme
Polynomial-time_approximation_scheme
Computational complexity
science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that can be solved
NL_(complexity)
Methodic assignment of colors to elements of a graph
Blanche (April 1947), "A three colour problem", Eureka, 21 Duffy, K.; O'Connell, N.; Sapozhnikov, A. (2008), "Complexity analysis of a decentralised graph
Graph_coloring
Mathematical proof about the permanent of matrices
a seminal result in computational complexity theory. In 1979, Leslie Valiant proved that the computational problem of computing the permanent of a matrix
♯P-completeness of 01-permanent
♯P-completeness_of_01-permanent
Notion in computational complexity theory
complexity for proving the hardness of counting problems, for counting complexity classes such as #P. Additionally, they are used in game complexity,
Parsimonious_reduction
Logic problem, AND of pairwise ORs
Dominic; Gale, Amy (2001), "The complexity of counting problems", Aspects of complexity: minicourses in algorithmics, complexity and computational algebra:
2-satisfiability
Open problem on 3x+1 and x/2 functions
and complexity". Computability. 1 (1): 19–56. doi:10.3233/COM-150032. Michel, Pascal (1993). "Busy beaver competition and Collatz-like problems". Archive
Collatz_conjecture
In computational complexity theory, the complexity class ⊕P (pronounced "parity P") is the class of decision problems solvable by a nondeterministic Turing
Parity_P
Pairing where no unchosen pair prefers each other over their choice
ISBN 978-1-4503-5559-9. MR 3826305. Irving, Robert W.; Leather, Paul (1986). "The complexity of counting stable marriages". SIAM Journal on Computing. 15 (3): 655–667. doi:10
Stable_matching_problem
Complexity class of problems
In computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and
NP-intermediate
Problem in quantum information science
to as quantum simulation) is a problem in quantum information science that attempts to find the computational complexity and quantum algorithms needed
Hamiltonian_simulation
Base-1 numeral system
solution. In computational complexity theory, unary numbering is used to distinguish strongly NP-complete problems from problems that are NP-complete but
Unary_numeral_system
Maciej; Ogihara, Mitsunori; Toda, Seinosuke (2003-07-28). "The complexity of counting self-avoiding walks in subgraphs of two-dimensional grids and hypercubes"
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Ancient algorithm for generating prime numbers
p equal 2, the smallest prime number. Enumerate the multiples of p by counting in increments of p from 2p to n, and mark them in the list (these will
Sieve_of_Eratosthenes
Approximate distinct counting algorithm
when switching from linear counting to the HLL counting. An empirical bias correction is proposed to mitigate the problem. A sparse representation of
HyperLogLog
Class of algorithms operating on data streams
elements problem is to output the set { i | fi > m/c }. Some notable algorithms are: Boyer–Moore majority vote algorithm Count-Min sketch Lossy counting Multi-stage
Streaming_algorithm
Algorithm using holographic reduction
the P versus NP problem and their impact on computational complexity theory. Although some of the general problems are #P-hard problems, the special cases
Holographic_algorithm
sometimes called ACC, is a class of computational models and problems defined in circuit complexity, a field of theoretical computer science. The class is defined
ACC0
Complexity of sending information in a distributed algorithm
science, communication complexity studies the amount of communication required to solve a problem when the input to the problem is distributed among two
Communication_complexity
Algorithm that employs a degree of randomness as part of its logic or procedure
and several complexity classes are studied. The most basic randomized complexity class is RP, which is the class of decision problems for which there
Randomized_algorithm
Overview of and topical guide to algorithms
computational complexity, and implementation in computer programs. Algorithm — finite sequence of instructions for solving a problem or performing a
Outline_of_algorithms
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
Accounting error wherein a transaction is counted more than once
necessarily create problems of double counting locally, but if we want to estimate world GDP, we may face double counting problems of some kind. Francois
Double_counting_(accounting)
Algorithm to be run on quantum computers
NP-complete problems in polynomial time. Quantum counting solves a generalization of the search problem. It solves the problem of counting the number of
Quantum_algorithm
Software metric used to measure the size of a computer program
automation of counting: since line of code is a physical entity, manual counting effort can be easily eliminated by automating the counting process. Small
Source_lines_of_code
Problem in physics and celestial mechanics
started historically with the two-body problem. The purpose of this section is to relate the real complexity in calculating any planetary forces. Note
N-body_problem
Study of resources used by an algorithm
computational complexity theory, which provides theoretical estimates for the resources needed by any algorithm which solves a given computational problem. These
Analysis_of_algorithms
Permutation of the elements of a set in which no element appears in its original position
the factorial of n and e ≈ 2.718281828... is Euler's number. The problem of counting derangements was first considered by Pierre Raymond de Montmort in
Derangement
Indian American professor of computer science (born 1957)
contributions to the classical maximum matching problem, and some key contributions to computational complexity theory, e.g., the isolation lemma, the Valiant–Vazirani
Vijay_Vazirani
In computational complexity theory, the element distinctness problem or element uniqueness problem is the problem of determining whether all the elements
Element_distinctness_problem
Chinese-American computer scientist
computational complexity theory. In recent years he has concentrated on the classification of computational counting problems, especially counting graph homomorphisms
Jin-Yi_Cai
On linear-time algorithms for graph logic
optimization or counting version, respectively. The proofs of Courcelle's theorem show a stronger result: not only can every (counting) monadic second-order
Courcelle's_theorem
Unit of measurement
function points – Adjusts for problem and data complexity with two questions that yield a somewhat subjective complexity measurement; simplifies measurement
Function_point
Mapping a graph onto itself without changing edge-vertex connectivity
like the graph isomorphism problem, the problem of finding a graph's automorphism group is known to belong to the complexity class NP, but not known to
Graph_automorphism
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
even with the addition of counting quantifiers, and thus of uniqueness quantification. This is a more powerful result, as counting quantifiers for high numerical
Two-variable_logic
Mathematical problem set on a chessboard
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution
Eight_queens_puzzle
Form of second-order logic
WS1S), the complexity of the decision problem is nonelementary. They could be obtained by performing a reduction of the emptiness problem of the star-free
Monadic_second-order_logic
Closure of nondeterministic space under complementation
theorem has become known as inductive counting. It has also been used to prove other theorems in computational complexity, including the closure of LOGCFL
Immerman–Szelepcsényi_theorem
the counting complexity of problems ranging from the Ising model in physics to the behavior of random instances of the Boolean satisfiability problem in
Nike_Sun
Optimization algorithms using quantum computing
the complexity and amount of data involved rise, more efficient ways of solving optimization problems are needed. Quantum computing may allow problems which
Quantum optimization algorithms
Quantum_optimization_algorithms
Mathematics award
All mathematical aspects of computer science, including computational complexity theory, logic of programming languages, analysis of algorithms, cryptography
IMU_Abacus_Medal
Concept in computational complexity theory
In computational complexity theory, the complexity class NEXPTIME (sometimes called NEXP) is the set of decision problems that can be solved by a non-deterministic
NEXPTIME
COUNTING PROBLEM-COMPLEXITY
COUNTING PROBLEM-COMPLEXITY
Girl/Female
Muslim/Islamic
Away from all Problems
Surname or Lastname
English
English : nickname from some fancied resemblance to the songbird (Emberiza spp.).German : patronymic from an unexplained Frisian-Lower Saxon personal name, or a derivative of Bunt- (see Bunten).Sarah Bunting (1686–1762), born in Matlock, Derbyshire, became a noted Quaker minister in Cross Wicks, NJ. It is believed but not certain that other members of her family, including her father, John Bunting, came with her to NJ sometime before 1704, when her marriage to William Murfin is recorded.
Boy/Male
Muslim
Problem solver
Surname or Lastname
English (southern counties)
English (southern counties) : apparently a variant of Hapgood.
Surname or Lastname
English (mainly northeastern counties)
English (mainly northeastern counties) : variant of Latham.
Surname or Lastname
English
English : patronymic from a short form of the personal name Cudbert (see Cuthbert).Americanized spelling of German Kötting or the variant Kotting (see Koetting).
Surname or Lastname
English (southern counties)
English (southern counties) : from a Middle English personal name, a pet form of Peter. Compare Parrott.
Surname or Lastname
English (eastern counties)
English (eastern counties) : unexplained.
Surname or Lastname
English (eastern counties)
English (eastern counties) : apparently a variant of German.
Surname or Lastname
English (southern counties)
English (southern counties) : unexplained.German : patronymic form of Old 2.
Surname or Lastname
English (eastern counties)
English (eastern counties) : unexplained. Possibly a variant of Masset (see Massett).
Boy/Male
Hindu, Indian
Counting
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Surname or Lastname
English
English : variant spelling of Countess.
Girl/Female
Indian, Telugu
Destroyer of Problems
Surname or Lastname
English (southern counties)
English (southern counties) : from Middle English woderson ‘son of the woodman’.
Surname or Lastname
English (northeastern counties)
English (northeastern counties) : unexplained. Compare Hedgepeth.
Boy/Male
Hindu, Indian
Problem
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Surname or Lastname
English
English : occupational name from Old English hunting, a derivative of huntian ‘to hunt’.
COUNTING PROBLEM-COMPLEXITY
COUNTING PROBLEM-COMPLEXITY
Boy/Male
Hindi
Sky god.
Boy/Male
Hindu, Indian
King of Wind and Truth
Biblical
vain pictures; divers picture
Girl/Female
Hindu, Indian
Newly Created
Boy/Male
Australian, Gaelic, Irish
Old; Ancient
Girl/Female
Arabic
Noble
Girl/Female
Indian, Telugu
Pray to God
Surname or Lastname
English
English : variant spelling of Keeton.
Girl/Female
Hindu
Boy/Male
Gujarati, Hindu, Indian, Kannada, Sanskrit, Telugu
Speaker
COUNTING PROBLEM-COMPLEXITY
COUNTING PROBLEM-COMPLEXITY
COUNTING PROBLEM-COMPLEXITY
COUNTING PROBLEM-COMPLEXITY
COUNTING PROBLEM-COMPLEXITY
n.
That by which anything is prepared for use, or set off to advantage; equipment; embellishment; setting; as, the mounting of a sword or diamond.
n.
A device or contrivance which serves to couple or connect adjacent parts or objects; as, a belt coupling, which connects the ends of a belt; a car coupling, which connects the cars in a train; a shaft coupling, which connects the ends of shafts.
n.
A sailing along a coast, or from port to port; a carrying on a coasting trade.
n.
Prowler; thief.
n.
One who proposes problems.
a.
Making or emitting sound; hence, sonorous; as, sounding words.
v. t.
To propose problems.
v. t.
To examine, as a wound, an ulcer, or some cavity of the body, with a probe.
n.
Same as Proleg.
n.
One of the fleshy legs found on the abdominal segments of the larvae of Lepidoptera, sawflies, and some other insects. Those of Lepidoptera have a circle of hooks. Called also proped, propleg, and falseleg.
n.
The sand, shells, or the like, that are brought up by the sounding lead when it has touched bottom.
imp. & p. p.
of Probe
n.
measurement by sounding; also, the depth so ascertained.
n.
A coat or covering; a layer of any substance, as a cover or protection; as, the coating of a retort or vial.
a.
Pompous; noisy; ostentatious; as, high-sounding words or titles.
n.
Any place or part of the ocean, or other water, where a sounding line will reach the bottom; -- usually in the plural.
n.
Anything which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular; or, in algebra, to find an unknown quantity.
a.
Speaking in a whining tone of voice; using technical or religious terms affectedly; affectedly pious; as, a canting rogue; a canting tone.
n.
A question proposed for solution; a matter stated for examination or proof; hence, a matter difficult of solution or settlement; a doubtful case; a question involving doubt.