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STATE COMPLEXITY

  • State complexity
  • 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

    State_complexity

  • Game 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

    Game_complexity

  • Kolmogorov complexity
  • Measure of algorithmic complexity

    of classical information theory. The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument

    Kolmogorov complexity

    Kolmogorov complexity

    Kolmogorov_complexity

  • Complexity class
  • 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

    Complexity class

    Complexity_class

  • 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

    Complexity

  • Computational complexity
  • 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

    Computational_complexity

  • NP (complexity)
  • 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)

    NP (complexity)

    NP_(complexity)

  • Alternating finite automaton
  • Markus; Kutrib, Martin (2011-03-01). "Descriptional and computational complexity of finite automata—A survey". Information and Computation. 209 (3): 456–470

    Alternating finite automaton

    Alternating_finite_automaton

  • Exponential time hypothesis
  • Unproven computational hardness assumption

    In computational complexity theory, the exponential time hypothesis (ETH) states that satisfiability of 3-CNF Boolean formulas (3-SAT) cannot be solved

    Exponential time hypothesis

    Exponential_time_hypothesis

  • Computational complexity theory
  • 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

  • Two-way finite automaton
  • Type of finite automaton in automata theory

    Sipser, who compared it to the P vs. NP problem in the computational complexity theory. Berman and Lingas discovered a formal relation between this problem

    Two-way finite automaton

    Two-way_finite_automaton

  • Programming complexity
  • Attribute of a software system

    measure the state of software, eventually concluding that the only practical solution is to use deterministic complexity models. The complexity of an existing

    Programming complexity

    Programming_complexity

  • Complex system
  • System composed of many interacting components

    theory, in which it prevails. As stated by Colander, the study of complexity is the opposite of the study of chaos. Complexity is about how a huge number of

    Complex system

    Complex_system

  • Quantum complexity theory
  • 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

    Quantum_complexity_theory

  • NL (complexity)
  • Computational complexity

    in computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that

    NL (complexity)

    NL_(complexity)

  • Parameterized 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

    Parameterized_complexity

  • Janusz Brzozowski (computer scientist)
  • Polish-Canadian computer scientist (1935–2019)

    for Complexity of Proper Prefix-Convex Regular Languages by J. Brzozowski and C. Sinnamon CIAA 2018 Sheng Yu Award for Best Paper for State Complexity of

    Janusz Brzozowski (computer scientist)

    Janusz Brzozowski (computer scientist)

    Janusz_Brzozowski_(computer_scientist)

  • Complementation of automata
  • Concept in theoretical computer science

    efficiently can we compute a complement automaton, e.g., in time complexity? State complexity: When complement automata exist, what is the smallest number

    Complementation of automata

    Complementation_of_automata

  • Complexity economics
  • 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

    Complexity_economics

  • L (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)

    L (complexity)

    L_(complexity)

  • Communication 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

    Communication_complexity

  • Law of conservation of complexity
  • Adage in human-computer interaction

    of conservation of complexity, also known as Tesler's Law, or Waterbed Theory, is an adage in human–computer interaction stating that every application

    Law of conservation of complexity

    Law_of_conservation_of_complexity

  • PP (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)

    PP (complexity)

    PP_(complexity)

  • Unambiguous finite automaton
  • Abstract machine model in computer science

    researched state complexity of basic regular operations on languages represented by UFA. They proved in particular that for every n {\displaystyle n} -state UFA

    Unambiguous finite automaton

    Unambiguous_finite_automaton

  • Certificate (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)

    Certificate_(complexity)

  • Russell Impagliazzo
  • American computer scientist

    the University of California, San Diego, specializing in computational complexity theory. Impagliazzo received a BA in mathematics from Wesleyan University

    Russell Impagliazzo

    Russell Impagliazzo

    Russell_Impagliazzo

  • Asymptotic computational complexity
  • Measurement of computational complexity

    computational complexity theory, asymptotic computational complexity is the use of asymptotic analysis for the estimation of the computational complexity of algorithms

    Asymptotic computational complexity

    Asymptotic_computational_complexity

  • BQP
  • 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

    BQP

    BQP

  • LH (complexity)
  • alternations, beginning with an existential state. LH is the union of all levels. Neil Immerman (1999). Descriptive Complexity. Springer. p. 85. v t e

    LH (complexity)

    LH_(complexity)

  • The Complexity of Songs
  • 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

    The_Complexity_of_Songs

  • NC (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)

    NC_(complexity)

  • Giovanni Pighizzini
  • Italian theoretical computer scientist

    scientist known for his work in formal language theory and particularly in state complexity of two-way finite automata. He earned his PhD in 1993 from the University

    Giovanni Pighizzini

    Giovanni_Pighizzini

  • Deterministic finite automaton
  • Finite-state machine

    construction with respect to the number of states has been determined in state complexity research. Since DFAs are equivalent to nondeterministic finite automata

    Deterministic finite automaton

    Deterministic finite automaton

    Deterministic_finite_automaton

  • DFA minimization
  • Task of transforming a deterministic finite automaton

    Assuming an efficient implementation of state sets and operations, this algorithm can be implemented with time complexity O(n+m), where n is the number of states

    DFA minimization

    DFA minimization

    DFA_minimization

  • FNP (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)

    FNP_(complexity)

  • Finite-state machine
  • Mathematical model of computation

    computer science, a finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical

    Finite-state machine

    Finite-state machine

    Finite-state_machine

  • Kai Salomaa
  • Finnish Canadian theoretical computer scientist

    theoretical computer scientist, known for his numerous contributions to the state complexity of finite automata. His highly cited 1994 joint paper with Yu and Zhuang

    Kai Salomaa

    Kai Salomaa

    Kai_Salomaa

  • Hamiltonian complexity
  • Hamiltonian complexity or quantum Hamiltonian complexity is a topic which deals with problems in quantum complexity theory and condensed matter physics

    Hamiltonian complexity

    Hamiltonian_complexity

  • Cognitive complexity
  • 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

    Cognitive complexity

    Cognitive_complexity

  • Cobham's thesis
  • Concept in computational complexity theory

    time; that is, if they lie in the complexity class P. In modern terms, it identifies tractable problems with the complexity class P. Formally, to say that

    Cobham's thesis

    Cobham's_thesis

  • QMA
  • Quantum Merlin Arthur

    state is rejected by the verifier with high probability. The relationship between QMA and BQP is analogous to the relationship between the complexity

    QMA

    QMA

  • Descriptional Complexity of Formal Systems
  • operation circuit complexity of Boolean functions and related measures succinctness of description of (finite) objects state complexity of finite automata

    Descriptional Complexity of Formal Systems

    Descriptional_Complexity_of_Formal_Systems

  • Ryan Williams (computer scientist)
  • American computer scientist (born 1969)

    is an American theoretical computer scientist working in computational complexity theory and algorithms. Williams graduated from the Alabama School of Mathematics

    Ryan Williams (computer scientist)

    Ryan Williams (computer scientist)

    Ryan_Williams_(computer_scientist)

  • Complexity and Contradiction in Architecture
  • Book by Robert Venturi

    Complexity and Contradiction in Architecture is a book by the American architect Robert Venturi. It was first published in 1966 by Museum of Modern Art

    Complexity and Contradiction in Architecture

    Complexity and Contradiction in Architecture

    Complexity_and_Contradiction_in_Architecture

  • Viliam Geffert
  • Slovak theoretical computer scientist

    his contributions to the computational complexity theory in sublogarithmic space and to the state complexity of two-way finite automata. He has also

    Viliam Geffert

    Viliam_Geffert

  • State space (computer science)
  • Set of all possible values of a system

    nonempty subset of N that contains the goal states. A state space has some common properties: complexity, where branching factor is important structure of

    State space (computer science)

    State space (computer science)

    State_space_(computer_science)

  • Information fluctuation complexity
  • Information-theoretic measure of complexity

    Information fluctuation complexity is an information-theoretic quantity defined as the fluctuation of information about entropy. It is derivable from fluctuations

    Information fluctuation complexity

    Information_fluctuation_complexity

  • Integrative complexity
  • Research psychometric

    Integrative complexity is a research psychometric that refers to the degree to which thinking and reasoning involve the recognition and integration of

    Integrative complexity

    Integrative complexity

    Integrative_complexity

  • Galactic algorithm
  • Classification of algorithm

    appear for problems that are so large they never occur, or the algorithm's complexity outweighs a relatively small gain in real-world performance. Galactic

    Galactic algorithm

    Galactic_algorithm

  • Structural complexity theory
  • Study of complexity classes

    computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather

    Structural complexity theory

    Structural complexity theory

    Structural_complexity_theory

  • List of computability and complexity topics
  • This is a list of computability and complexity topics, by Wikipedia page. Computability theory is the part of the theory of computation that deals with

    List of computability and complexity topics

    List_of_computability_and_complexity_topics

  • IP (complexity)
  • 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)

    IP (complexity)

    IP_(complexity)

  • Complexity theory and organizations
  • Application of complexity theory to strategy

    Complexity theory and organizations, also called complexity strategy or complex adaptive organizations, is the use of the study of complexity systems

    Complexity theory and organizations

    Complexity_theory_and_organizations

  • PL (complexity)
  • 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)

    PL_(complexity)

  • UML state machine
  • State machines and generalizations in UML

    phenomenon known as state and transition explosion, the complexity of a traditional FSM tends to grow much faster than the complexity of the system it describes

    UML state machine

    UML_state_machine

  • Randomized algorithm
  • Algorithm that employs a degree of randomness as part of its logic or procedure

    Carlo algorithms are considered, and several complexity classes are studied. The most basic randomized complexity class is RP, which is the class of decision

    Randomized algorithm

    Randomized_algorithm

  • Theoretical computer science
  • Subfield of computer science and mathematics

    variety of topics including algorithms, data structures, computational complexity, parallel and distributed computation, probabilistic computation, quantum

    Theoretical computer science

    Theoretical computer science

    Theoretical_computer_science

  • State (polity)
  • Type of political organization

    increase in the organizational complexity of the central government (bureaucracy). The transition to this modern state was possible in Europe around 1600

    State (polity)

    State_(polity)

  • Krohn–Rhodes theory
  • 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

    Krohn–Rhodes_theory

  • Proof 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

    Proof_complexity

  • QIP (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)

    QIP_(complexity)

  • DTIME
  • Deterministic time, in computational complexity theory

    In computational complexity theory, DTIME (or TIME) is the computational resource of computation time for a deterministic Turing machine. It represents

    DTIME

    DTIME

  • Social complexity
  • Conceptual framework

    sociology, social complexity is a conceptual framework used in the analysis of society. In the sciences, contemporary definitions of complexity are found in

    Social complexity

    Social complexity

    Social_complexity

  • ELEMENTARY
  • This complexity class can be characterized by a certain class of "iterated stack automata", pushdown automata that can store the entire state of a lower-order

    ELEMENTARY

    ELEMENTARY

  • Nation state
  • Political term for a state that is based around a nation

    A nation state, or nation-state, is a political entity in which the state (a centralized political organization ruling over a population within a territory)

    Nation state

    Nation_state

  • Perturbational Complexity Index
  • Measure of the level of consciousness

    Perturbational Complexity Index (PCI) is a quantitative measure used in neuroscience to assess the level of consciousness based on the complexity of brain responses

    Perturbational Complexity Index

    Perturbational Complexity Index

    Perturbational_Complexity_Index

  • ♯P
  • Complexity class

    In computational complexity theory, the complexity class #P (pronounced "sharp P" or, sometimes "number P" or "hash P") is the set of the counting problems

    ♯P

    ♯P

  • PLS (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)

    PLS_(complexity)

  • Fine grained complexity
  • Subfield of computational complexity theory

    Fine-grained complexity is a subfield of computational complexity theory that studies the time required to solve computational problems, especially those

    Fine grained complexity

    Fine_grained_complexity

  • Analysis of algorithms
  • Study of resources used by an algorithm

    the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to

    Analysis of algorithms

    Analysis of algorithms

    Analysis_of_algorithms

  • Self-verifying finite automaton
  • as deterministic finite automata (DFA) and NFA but have different state complexity. An SVFA is represented formally by a 6-tuple, A=(Q, Σ, Δ, q0, Fa,

    Self-verifying finite automaton

    Self-verifying_finite_automaton

  • Valiant–Vazirani theorem
  • If there is a polynomial time algorithm for unambiguous-SAT, then NP equals RP

    The Valiant–Vazirani theorem is a theorem in computational complexity theory stating that if there is a polynomial time algorithm for Unambiguous-SAT

    Valiant–Vazirani theorem

    Valiant–Vazirani_theorem

  • Fagin's theorem
  • Existential second order logic captures NP

    oldest result of descriptive complexity theory, a branch of computational complexity theory that characterizes complexity classes in terms of logic-based

    Fagin's theorem

    Fagin's_theorem

  • Sample 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

    Sample_complexity

  • Von Neumann universal constructor
  • Self-replicating cellular automaton

    machine whose complexity could grow automatically akin to biological organisms under natural selection. He asked what is the threshold of complexity that must

    Von Neumann universal constructor

    Von Neumann universal constructor

    Von_Neumann_universal_constructor

  • Tempo
  • Musical concept indicating to the speed of interpretation

    are perceived in the simplest way. From the viewpoint of Kolmogorov's complexity theory, this means a representation of the data that minimizes the amount

    Tempo

    Tempo

    Tempo

  • Hash table
  • Associative array for storing key–value pairs

    probing sequence. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the

    Hash table

    Hash table

    Hash_table

  • Irreducible 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

    Irreducible_complexity

  • Dani Bassett
  • American physicist

    Nelson; B A Mueller; J Camchong; K O Lim (2012). "Altered resting state complexity in schizophrenia". NeuroImage. 59 (3): 2196–2207. doi:10.1016/j.neuroimage

    Dani Bassett

    Dani_Bassett

  • Blum's speedup theorem
  • 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

    Blum's_speedup_theorem

  • Strategy
  • Discipline for achieving objectives against unpredictability, complexity, and ambiguity

    extension of the mindset or ideological perspective of the organization. Complexity theorists define strategy as the unfolding of the internal and external

    Strategy

    Strategy

  • Evil number
  • Class of binary number

    Foundation Charlier, Émilie; Cisternino, Célia; Massuir, Adeline (2019), "State complexity of the multiples of the Thue-Morse set", Proceedings Tenth International

    Evil number

    Evil_number

  • Palestine
  • Country in West Asia

    Convention]? A.Many experts say that it does, though there is considerable complexity surrounding the particular criteria. & Q. What about recognition? A.The

    Palestine

    Palestine

    Palestine

  • Specified complexity
  • 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

    Specified_complexity

  • Failed state
  • State that has lost its ability to govern

    A failed state is a state that has lost its ability to fulfill fundamental security and development functions, lacking effective control over its territory

    Failed state

    Failed_state

  • Magic state distillation
  • Quantum computing algorithm

    Magic state distillation is a method for creating more accurate quantum states from multiple noisy ones, which is important for building fault tolerant

    Magic state distillation

    Magic_state_distillation

  • 2-EXPTIME
  • Complexity class

    In computational complexity theory, the complexity class 2-EXPTIME (sometimes called 2-EXP, sometimes also written 2EXPTIME) is the set of all decision

    2-EXPTIME

    2-EXPTIME

  • Oracle machine
  • Abstract machine used to study decision problems

    In complexity theory and computability theory, an oracle machine is an abstract machine that can query a black box called an oracle, which is able to give

    Oracle machine

    Oracle_machine

  • Fast Fourier transform
  • Discrete Fourier transform algorithm

    of sparse (mostly zero) factors. As a result, it manages to reduce the complexity of computing the DFT from O(n2), which arises if one simply applies the

    Fast Fourier transform

    Fast Fourier transform

    Fast_Fourier_transform

  • Model of computation
  • Mathematical model describing how an output of a function is computed given an input

    computational complexity of algorithms. Models differ in their expressive power; for example, each function that can be computed by a finite-state machine can

    Model of computation

    Model_of_computation

  • Breadth-first search
  • Algorithm to search the nodes of a graph

    graph of German cities (upper diagram) starting from Frankfurt. The time complexity can be expressed as O(|V|+|E|), as every vertex and every edge will be

    Breadth-first search

    Breadth-first search

    Breadth-first_search

  • Arithmetic circuit complexity
  • 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

    Arithmetic_circuit_complexity

  • P versus NP problem
  • Unsolved problem in computer science

    P = NP problem can also be stated as a question about expressive power in descriptive complexity, which characterizes complexity classes by logics over finite

    P versus NP problem

    P_versus_NP_problem

  • Complexity and Real Computation
  • 1998 non-fiction book

    Complexity and Real Computation is a book on the computational complexity theory of real computation. It studies algorithms whose inputs and outputs are

    Complexity and Real Computation

    Complexity_and_Real_Computation

  • Peter Turchin
  • Russian-American scientist (born 1957)

    and evolutionary biology and mathematics. He is a project leader at the Complexity Science Hub Vienna and a research associate at the School of Anthropology

    Peter Turchin

    Peter Turchin

    Peter_Turchin

  • Chris Pratt
  • American actor (born 1979)

    sweetheart", criticizing his "safe" screen presence that lacked the depth and complexity necessary for his cinematic roles. Other critics have thought otherwise;

    Chris Pratt

    Chris Pratt

    Chris_Pratt

  • Alternating Turing machine
  • Abstract computation model

    In computational complexity theory, an alternating Turing machine (ATM) is a non-deterministic Turing machine (NTM) with a rule for accepting computations

    Alternating Turing machine

    Alternating_Turing_machine

  • William E. Doll Jr.
  • American educator, author and curriculum theorist

    chaos theory and complexity and their implications for school curriculum. Doll is among the first group of scholars who introduced complexity thinking to education

    William E. Doll Jr.

    William_E._Doll_Jr.

  • Unified state power
  • Political power principle of communist states

    Unified state power is a Marxist–Leninist principle on communist state power that was developed in opposition to the fusion and separation of powers, and

    Unified state power

    Unified_state_power

  • Eventual consistency
  • Consistency model used in distributed computing to achieve high availability

    Eventual consistency faces criticism for adding complexity to distributed software applications. This complexity arises because eventual consistency provides

    Eventual consistency

    Eventual_consistency

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