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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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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)
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)
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)
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
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
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
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 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)
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
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)
computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather
Structural_complexity_theory
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
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)
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
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
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)
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 ) {\displaystyle O(n+m)}
DFA_minimization
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
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
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
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 psychology
Cognitive complexity describes cognition along a simplicity-complexity axis. It is the subject of academic study in fields including personal construct
Cognitive_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, Polynomial Local Search (PLS) is a complexity class that models the difficulty of finding a locally optimal solution
PLS_(complexity)
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
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)
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
Computational complexity
in computer science In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems that
NL_(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
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)
Hamiltonian complexity or quantum Hamiltonian complexity is a topic which deals with problems in quantum complexity theory and condensed matter physics
Hamiltonian_complexity
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
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
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
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)
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
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
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
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
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
American professional electronic sports organization
Complexity Gaming, formerly stylized as compLexity, was an American esports franchise headquartered in Frisco, Texas. The franchise was founded in 2003
Complexity_Gaming
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
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
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
Complexity class used in circuit complexity
theoretical computer science, and specifically computational complexity theory and circuit complexity, TC0 (Threshold Circuit) is the first class in the hierarchy
TC0
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
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
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
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
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
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
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
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
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
Complexity class of approximable problems
In computational complexity theory, the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time
APX
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
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
Country in East Asia
Simulation, plus Econophysics Colloquium 2014. Springer Proceedings in Complexity. pp. 151–162. doi:10.1007/978-3-319-20591-5_14. ISBN 978-3-319-20590-8
Japan
A state hospital is a hospital funded and operated by the government of a state. In some countries, such as South Africa, the term is synonymous with
State_hospital
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
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
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
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
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
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
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
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
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
U.S. state
referendum. The former constitution was particularly criticized for its complexity and length intentionally codifying segregation and racism. Alabama's government
Alabama
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
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
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
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
Congolese rebel leader
Retrieved 5 June 2020. "The CNPSC Rebellion - Social Marginalization and State Complexity in South Kivu" (PDF). Congo Research Group. February 2019. Retrieved
William_Yakutumba
Algorithm used for pathfinding and graph traversal
major practical drawback is its O ( b d ) {\displaystyle O(b^{d})} space complexity where d is the depth of the shallowest solution (the length of the shortest
A*_search_algorithm
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
Basic programming language construct
"Operators". doc.perl6.org. Pribavkina, Elena V.; Rodaro, Emanuele (2010). "State Complexity of Prefix, Suffix, Bifix and Infix Operators on Regular Languages"
Operator (computer programming)
Operator_(computer_programming)
U.S. state
dramatically and there is strong evidence of a growing cultural and political complexity. Many Coles Creek sites were erected over earlier Woodland period mortuary
Louisiana
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
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
Quantum algorithm
Bernstein–Vazirani algorithm was designed to prove an oracle separation between complexity classes BQP and BPP. Given an oracle that implements a function f : {
Bernstein–Vazirani_algorithm
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
travel, tourism, insurance
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