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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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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)
Computational complexity
in computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that
NL_(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
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
Hamiltonian complexity or quantum Hamiltonian complexity is a topic which deals with problems in quantum complexity theory and condensed matter physics
Hamiltonian_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
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
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)
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
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
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
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)
In computational complexity, the logarithmic time hierarchy (LH) is the complexity class of all computational problems solvable in a logarithmic amount
LH_(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
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
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
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)
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)
computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather
Structural_complexity_theory
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
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
American professional electronic sports organization
Complexity Gaming, formerly stylized as compLexity, is an American esports franchise headquartered in Frisco, Texas. The franchise was founded in 2003
Complexity_Gaming
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
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)
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
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
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
Quantum Merlin Arthur
abbreviation for Quantum Merlin Arthur, refers to a complexity class in computational complexity theory. It is the set of all formal languages that satisfy
QMA
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
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
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
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
Task of transforming a deterministic finite automaton
Câmpeanu, Cezar; Culik, Karel II; Salomaa, Kai; Yu, Sheng (2001), "State Complexity of Basic Operations on Finite Languages", Automata Implementation,
DFA_minimization
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)
French philosopher and sociologist (1921–2026)
of the theory of information who has been recognised for his work on complexity and Complex Thought, and for his scholarly contributions to such diverse
Edgar_Morin
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)
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
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 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)
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
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
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
Congolese rebel leader
Sovereignty of Congo "The CNPSC Rebellion - Social Marginalization and State Complexity in South Kivu" (PDF). Congo Research Group. February 2019. Retrieved
William_Yakutumba
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
Mathematical model of computation
Glenn (1989). Theory of Computation: Formal Languages, Automata, and Complexity. Redwood City, California: Benjamin/Cummings Publish Company, Inc.
Finite-state_machine
Both deterministic and nondeterministic machines can solve more problems given more space
In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines
Space_hierarchy_theorem
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)
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
Unsolved problem in computer science
could be automated. The relation between the complexity classes P and NP is studied in computational complexity theory, the part of the theory of computation
P_versus_NP_problem
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
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
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
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
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
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
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
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
Book by J. Stephen Lansing
1980 book Negara: The Theatre State in Nineteenth-Century Bali. Heider, Karl G. (2008). "Perfect Order: Recognizing Complexity in Bali. By J. Stephen Lansing
Perfect_Order
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
Class of thermodynamic models
reasons, but since its development other equations of only slightly greater complexity have been since developed, many of which are far more accurate. The van
Cubic_equations_of_state
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
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
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
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
Complexity Analyzer (L2SCA) developed by Xiaofei Lu at the Pennsylvania State University, is a computational tool which produces syntactic complexity
L2 Syntactic Complexity Analyzer
L2_Syntactic_Complexity_Analyzer
Algorithm analysis method
slight noises and imprecisions. Smoothed complexity results are strong probabilistic results, roughly stating that, in every large enough neighbourhood
Smoothed_analysis
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
Bounded-error probabilistic polynomial time is contained in the polynomial time hierarchy
In computational complexity theory, the Sipser–Lautemann theorem or Sipser–Gács–Lautemann theorem states that bounded-error probabilistic polynomial (BPP)
Sipser–Lautemann_theorem
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
American complexity theorist (1941–2021)
his research on structural complexity theory, the study of computational complexity in terms of the relation between complexity classes rather than individual
Alan_Selman
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
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
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
Study of computation
models of computation. The second question is addressed by computational complexity theory, which studies the time and space costs associated with different
Computer_science
Political power principle of communist states
formally granted a monopoly on legislative powers, justified by the growing complexity of the Soviet economy and the need for more precise institutional boundaries
Unified_state_power
In computational complexity theory, the complexity class E L E M E N T A R Y {\displaystyle {\mathsf {ELEMENTARY}}} consists of the decision problems
ELEMENTARY
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
U.S. state flag
incorporated the then state seal, which included imagery considered controversial to some.[who?] Criticism over the flag's complexity and depiction of Indigenous
Flag_of_Minnesota
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
Canadian-American computer scientist
Canadian-American mathematician and computer scientist specializing in computational complexity theory. She is currently Jeffrey L. and Brenda Bleustein Professor of
Toniann_Pitassi
Theorem in computational complexity theory
computational complexity theory, the PCP theorem (also known as the PCP characterization theorem) states that every decision problem in the NP complexity class
PCP_theorem
Laws of individual U.S. states, which are separate sovereigns
complained about how the diversity and volume of state law hampered interstate trade and introduced complexity and inconvenience into virtually any interstate
State_law_(United_States)
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
Conjecture in quantum gravity
quantum complexity theory, the complexity equals action duality (CA-duality) is the conjecture that the gravitational action of any semiclassical state with
CA-duality
Country in Southeast Asia and Oceania
Goldstein 2024, pp. 11, 14, 56–57. "Indonesia". The Observatory of Economic Complexity. 2023. Retrieved 8 May 2025. Suryanta, B. (2021). Indonesia's Integration
Indonesia
Austrian nonprofit research organization
The Complexity Science Hub Vienna (CSH) is a Vienna-based research organisation with the aim to bundle, coordinate and advance the research of complex
Complexity_Science_Hub
STATE COMPLEXITY
STATE COMPLEXITY
Surname or Lastname
English
English : unexplained.
Girl/Female
English Scandinavian Anglo Saxon Irish
Brings joy.
Girl/Female
American, Anglo, Australian, British, English, Finnish, Irish, Scandinavian
Light Hearted; Cheerful; Pleasant and Bright; Brings Joy; Bright; Great; Measure of Land
Boy/Male
Celebrity, Hindu, Indian, Telugu
State
Surname or Lastname
English
English : metonymic occupational name for a slater, from Middle English slate ‘slate’.
Surname or Lastname
English and Irish
English and Irish : variant of Stacey.
Boy/Male
Arabic
Power; State
Girl/Female
Muslim
Wealth, Empire, State
Surname or Lastname
English
English : from the Old English personal name TÄta, possibly a short form of various compound names with the obscure first element tÄt, or else a nursery formation. This surname is common and widespread in Britain; the chief area of concentration is northeastern England, followed by northern Ireland.
Girl/Female
Indian, Kashmiri
State Honour
Boy/Male
Arabic
State; Condition
Boy/Male
Hindu, Indian
State; Country
Boy/Male
Arabic
Leadership; State
Male
English
English surname transferred to unisex forename use, TATE means "cheerful."
Boy/Male
English Scandinavian American Irish Native American
Cheerful.
Boy/Male
Arabic
Leadership; State
Boy/Male
Arabic
Power; State
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, English, Finnish, German, Indian, Irish, Norse, Scandinavian
To be Cheerful; Great; Measure of Land; Great Talker
Surname or Lastname
Indian (northern states)
Indian (northern states) : Hindu name meaning ‘lamp’, from Sanskrit dīpa. It occurs commonly as the final element of compound personal names, e.g. in Kuldeep ‘light of the family’. Subsequently, it appears to have evolved into a surname.English : presumably from the adjective deep, either a topographic name for someone who lived in a deep valley, or perhaps a nickname for a ‘deep’, thoughtful person.
Boy/Male
Arabic
State; Dignity
STATE COMPLEXITY
STATE COMPLEXITY
Boy/Male
Tamil
Fiery, Passionate, Married, One who wins the fire
Girl/Female
Indian, Tamil
Goddess Laxmi
Boy/Male
American, Australian, British, English
Beacon Hill; Broom Covered Hill
Boy/Male
Tamil
Lord
Boy/Male
Hindu
Companionate person, Kind to others
Boy/Male
Hindi
Prosperous.
Girl/Female
Hindu, Indian
Goddess
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu, Traditional
Small Fragrant Flower; Moonlight; A Jasmine Flower
Girl/Female
Tamil
Ilavalagi | இலாவாலாகீ
Young and beautiful
Boy/Male
Muslim/Islamic
Protector
STATE COMPLEXITY
STATE COMPLEXITY
STATE COMPLEXITY
STATE COMPLEXITY
STATE COMPLEXITY
n.
Rank; condition; quality; as, the state of honor.
n.
To break in a stave or the staves of; to break a hole in; to burst; -- often with in; as, to stave a cask; to stave in a boat.
n.
One of several marked phases or periods in the development and growth of many animals and plants; as, the larval stage; pupa stage; zoea stage.
v. t.
To pierce or wound with a stake.
n.
Any body of men united by profession, or constituting a community of a particular character; as, the civil and ecclesiastical states, or the lords spiritual and temporal and the commons, in Great Britain. Cf. Estate, n., 6.
v. t.
To place, as a statue; to form a statue of; to make into a statue.
n.
See Skate, for the foot.
imp. & p. p.
of State
n.
The bodies that constitute the legislature of a country; as, the States-general of Holland.
a.
Belonging to the state, or body politic; public.
n.
Estate, possession.
a.
Recurring at regular time; not occasional; as, stated preaching; stated business hours.
v. t.
To exhibit upon a stage, or as upon a stage; to display publicly.
v. t.
To endow with an estate.
v. t.
To express the particulars of; to set down in detail or in gross; to represent fully in words; to narrate; to recite; as, to state the facts of a case, one's opinion, etc.
n.
The state; the general body politic; the common-wealth; the general interest; state affairs.
n.
One who states.
v. t.
To cover with slate, or with a substance resembling slate; as, to slate a roof; to slate a globe.
n.
Estate; state.
v. t.
To mark the limits of by stakes; -- with out; as, to stake out land; to stake out a new road.