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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
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
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
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)
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
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
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
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
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
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
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
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)
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
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 (logarithmic space)
In computational complexity theory, L (also known as LSPACE, LOGSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved
L_(complexity)
Complexity of sending information in a distributed algorithm
In theoretical computer science, communication complexity studies the amount of communication required to solve a problem when the input to the problem
Communication_complexity
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
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)
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
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)
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
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
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
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)
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
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)
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
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
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
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)
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
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
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 psychology
Cognitive complexity describes cognition along a simplicity-complexity axis. It is the subject of academic study in fields including personal construct
Cognitive_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
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
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
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)
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
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
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)
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
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
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
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
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
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)
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
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)
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
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
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
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)
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
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
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)
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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