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Type of finite automaton in automata theory
automata theory, a two-way finite automaton is a finite automaton that is allowed to re-read its input. A two-way deterministic finite automaton (2DFA) is an
Two-way_finite_automaton
Finite-state machine
deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state
Deterministic finite automaton
Deterministic_finite_automaton
Type of finite-state machine in automata theory
In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its
Nondeterministic finite automaton
Nondeterministic_finite_automaton
Self-operating machine
An automaton (/ɑːˈtɑːmətɑːn/ ; pl.: automata or automatons) is a relatively self-operating machine or control mechanism designed to automatically follow
Automaton
In automata theory, an alternating finite automaton (AFA) is a nondeterministic finite automaton whose transitions are divided into existential and universal
Alternating_finite_automaton
Quantum analog of probabilistic automata
QFA, there are two noteworthy generalizations that should be mentioned and understood. The first is the non-deterministic finite automaton (NFA). In this
Quantum_finite_automaton
Type of automaton
nested stack automaton allows full access, and also allows stacked values to be entire sub-stacks rather than just single finite symbols. A finite-state machine
Pushdown_automaton
computer science, the probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given
Probabilistic_automaton
State machine for tree structures
automata, finite tree automata (FTA) can be either a deterministic automaton or not. According to how the automaton processes the input tree, finite tree automata
Tree_automaton
Discrete model of computation
and microstructure modeling. A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in
Cellular_automaton
nested stack automaton is a finite automaton that can make use of a stack containing data that can be additional stacks. Like a stack automaton, a nested
Nested_stack_automaton
Formal language that can be expressed using a regular expression
the language accepted by an alternating finite automaton it is the language accepted by a two-way finite automaton it can be generated by a prefix grammar
Regular_language
automata theory, a tagged deterministic finite automaton (TDFA) is an extension of deterministic finite automaton (DFA). In addition to solving the recognition
Tagged Deterministic Finite Automaton
Tagged_Deterministic_Finite_Automaton
Concept in theoretical computer science
depends on the automaton formalism used to represent the input automaton A and the complement automaton. For instance, if A is a finite automaton, then a complement
Complementation_of_automata
automata theory, a self-verifying finite automaton (SVFA) is a special kind of a nondeterministic finite automaton (NFA) with a symmetric kind of nondeterminism
Self-verifying finite automaton
Self-verifying_finite_automaton
Study of abstract machines and automata
of operations automatically. An automaton with a finite number of states is called a finite automaton (FA) or finite-state machine (FSM). The figure on
Automata_theory
Pattern that has no predecessors
the automaton (usually a one- or two-dimensional infinite square lattice of cells). However, for any Garden of Eden there is at least one finite pattern
Garden of Eden (cellular automaton)
Garden_of_Eden_(cellular_automaton)
Finite state machine with two tapes (input, output)
with an ordinary finite-state automaton, which has a single tape. An FST is a type of finite-state automaton (FSA) that maps between two sets of symbols
Finite-state_transducer
Elementary cellular automaton
The Rule 110 cellular automaton (often called simply Rule 110) is an elementary cellular automaton with interesting behavior on the boundary between stability
Rule_110
Cellular automaton that can be run backwards
approximate reversibility." A cellular automaton is defined by its cells (often a one- or two-dimensional array), a finite set of values or states that can
Reversible_cellular_automaton
Mathematical structure
infinite-tree automaton is a state machine that deals with infinite tree structures. It can be seen as an extension of top-down finite-tree automata to
Infinite-tree_automaton
Deterministic finite automaton accepting set of all suffixes of particular string
string. In terms of automata theory, a suffix automaton is the minimal partial deterministic finite automaton that recognizes the set of suffixes of a given
Suffix_automaton
Israeli mathematician and computer scientist (1931–2026)
paper "Finite Automata and Their Decision Problems". Soon, using nondeterministic automata, they were able to re-prove Kleene's result that finite state
Michael_O._Rabin
Kind of cellular automaton
conservation laws. A block cellular automaton consists of the following components: A regular lattice of cells A finite set of the states that each cell
Block_cellular_automaton
Mathematics concept
computability theory, an elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the
Elementary_cellular_automaton
Algorithm to transform a regular expression into a finite automaton
transforming a regular expression into an equivalent nondeterministic finite automaton (NFA). This NFA can be used to match strings against the regular expression
Thompson's_construction
Automaton which either accepts or rejects infinite inputs
C=(Q_{C},\Sigma ,\Delta _{C},I_{C},{F}_{C})} be a finite automaton. Union: There is a Büchi automaton that recognizes the language L ( A ) ∪ L ( B ) .
Büchi_automaton
Two-dimensional cellular automaton
of Life (sometimes abbreviated as CGoL) or simply Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is
Conway's_Game_of_Life
Formal language concept
a⟩⟨b⟨aa⟩⟨bcc⟩⟨ca. A nested word automaton has a finite number of states, and operates in almost the same way as a deterministic finite automaton on classical strings:
Nested_word
defined as a (finite or infinite) set of strings that can be described by one of the mathematical formalisms called "finite automaton", "regular grammar"
Induction of regular languages
Induction_of_regular_languages
Term in distributed computing
set of states of automaton A, denoted states(A), need not be finite. This is a significant generalization of the usual notion of finite automata, as it
Input/output_automaton
Method for making finite automata deterministic
standard method for converting a nondeterministic finite automaton (NFA) into a deterministic finite automaton (DFA) that recognizes the same formal language
Powerset_construction
Finite-state machine where edges carry weights
and formal language theory, a weighted automaton or weighted finite-state machine is a generalization of a finite-state machine in which the edges have
Weighted_automaton
Reversible block cellular automaton
periodic boundary conditions (so that the entire space of the cellular automaton is finite) initial fields of random cells that are sufficiently smaller than
Critters_(cellular_automaton)
Deterministic finite automaton Nondeterministic finite automaton Generalized nondeterministic finite automaton Regular language Pumping lemma Myhill–Nerode
List of computability and complexity topics
List_of_computability_and_complexity_topics
Programming paradigm based on formal automatons
it is thought of as a model of a finite-state machine (FSM) or any other (often more complicated) formal automaton (see automata theory). Sometimes a
Automata-based_programming
Type of shift space studied in ergodic theory
the set of labellings of paths through an automaton: a subshift of finite type then corresponds to an automaton which is deterministic. Such systems correspond
Subshift_of_finite_type
kinds of finite automata. The classical result in the area is that simulating an n {\displaystyle n} -state nondeterministic finite automaton by a deterministic
State_complexity
Sequence of characters that forms a search pattern
construct a nondeterministic finite automaton (NFA), which is then made deterministic and the resulting deterministic finite automaton (DFA) is run on the target
Regular_expression
Table in automata theory and sequential logic
showing what state (or states in the case of a nondeterministic finite automaton) a finite-state machine will move to, based on the current state and other
State-transition_table
Diagram of behavior of finite state systems
state diagram for a finite automaton (FA) is a directed graph with the following elements (Q, Σ, Z, δ, q0, F): Vertices Q: a finite set of states, normally
State_diagram
List of unsolved computational problems
problem: How many states are needed in a deterministic finite automaton that behaves differently on two given strings of length n {\displaystyle n} ? What
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Sequence of words formed by specific rules
expression; those strings accepted by some automaton, such as a Turing machine or finite-state automaton; those strings for which some decision procedure
Formal_language
Computation model defining an abstract machine
can perform to those of a linear bounded automaton if the tape was proportional to the input size, or finite-state machine if it was strictly fixed-length
Turing_machine
A read-only Turing machine or two-way deterministic finite-state automaton (2DFA) is class of models of computability that behave like a standard Turing
Read-only_Turing_machine
Ability to solve a problem by an effective procedure
Deterministic finite automaton (DFA) Also called a finite-state machine. All real computing devices in existence today can be modeled as a finite-state machine
Computability
Cellular automaton pattern
In a cellular automaton, a puffer train, or simply puffer, is a finite pattern that moves itself across the "universe", leaving debris ("ash") behind.
Puffer_train
problem, one is given as input a deterministic finite automaton, and must find an equivalent automaton with as few states as possible. Hopcroft's algorithm
Partition_refinement
Excitable cellular automaton
As in a typical two dimensional cellular automaton, consider a rectangular grid, or checkerboard pattern, of "cells". It can be finite or infinite in extent
Greenberg–Hastings cellular automaton
Greenberg–Hastings_cellular_automaton
Type of cellular automaton
cellular automaton (CA) is a discrete dynamical system consisting of a uniform (finite or infinite) grid of cells. Each cell can be in only one of a finite number
Quantum dot cellular automaton
Quantum_dot_cellular_automaton
Connectivity measure in graph theory
accepted by the automaton is the language accepted by the automaton A. When speaking of digraph properties of a nondeterministic finite automaton A with state
Cycle_rank
Infinite sequence of terms characterized by a finite automaton
characterized by a finite automaton. The n-th term of an automatic sequence a(n) is a mapping of the final state reached in a finite automaton accepting the
Automatic_sequence
Type of formal grammar
and those of a nondeterministic finite automaton, such that the grammar generates exactly the language the automaton accepts. Hence, the right-regular
Regular_grammar
Regular expression denial-of-service attack
After building the automaton, several possibilities exist: the engine may convert it to a deterministic finite-state automaton (DFA) and run the input
ReDoS
Searching for patterns in text
approach, backtracking is avoided by constructing a deterministic finite automaton (DFA) that recognizes a stored search string. These are expensive to
String-searching_algorithm
Data structure
to each word is not required), a minimal deterministic acyclic finite state automaton (DAFSA) would use less space than a trie or a ternary search tree
Ternary_search_tree
Numerical method for solving physical or engineering problems
finite element Isogeometric analysis Lattice Boltzmann methods List of finite element software packages Meshfree methods Movable cellular automaton Multidisciplinary
Finite_element_method
and theoretical computer science, a semiautomaton is a deterministic finite automaton having inputs but no output. It consists of a set Q of states, a set
Semiautomaton
State machines and generalizations in UML
as UML statechart, is an extension of the mathematical concept of a finite automaton in computer science applications as expressed in the Unified Modeling
UML_state_machine
Cellular automaton
Abelian sandpile model. The model is a cellular automaton. In its original formulation, each site on a finite grid has an associated value that corresponds
Abelian_sandpile_model
Idea that the universe is fundamentally computational or informational
best-known form takes the universe to be a cellular automaton: a lattice of cells, each in one of finitely many states, updating in discrete steps according
Digital_physics
Approach to the study of finite semigroups and automata
method for decomposing a (deterministic) finite automaton into "simple" components that are themselves finite automata. This joint work, which has implications
Krohn–Rhodes_theory
Elementary cellular automaton
90. Rule 90 (on finite rows of cells) can also be simulated by the block oscillators of the two-dimensional Life-like cellular automaton B36/S125, also
Rule_90
we can see the graph database as a finite automaton, also represent the regular path query as a finite automaton, and check if a suitable path exists
Regular_path_query
group is surjunctive. A cellular automaton consists of a regular system of cells, each containing a symbol from a finite alphabet, together with a uniform
Surjunctive_group
Data structure
search to be performed symbol-by-symbol The suffix automaton, the minimal deterministic finite automaton that recognizes substrings of a given text, closely
Substring_index
Type of pattern that does not change from one generation to the next
large grid, no more than half of the cells in the plane can be live. For finite square grids, greater densities can be achieved. For instance, the maximum
Still life (cellular automaton)
Still_life_(cellular_automaton)
Elementary cellular automaton
majority problem is the problem of constructing a cellular automaton that, when run on any finite set of cells, can compute the value held by a majority of
Rule_184
right), or a character from an alphabet picked off the input tape of a finite automaton, while the graph might represent the flow of information or state transitions
Noncommutative signal-flow graph
Noncommutative_signal-flow_graph
Mathematics concept
pioneered an alternative approach in which a deterministic finite automaton is used to read symbols of two input strings and produce a (long but not optimal)
Chvátal–Sankoff_constants
Academic subfield of computer science
the class of formal languages they are able to recognize. An automaton can be a finite representation of a formal language that may be an infinite set
Theory_of_computation
Formal language generated by context-free grammar
there is a direct way to produce a pushdown automaton for the grammar (and thereby the corresponding language), though going the other way (producing a grammar
Context-free_language
Farrell–Jones conjecture Finite lattice representation problem: is every finite lattice isomorphic to the congruence lattice of some finite algebra? Goncharov
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Fractal composed of triangles
standard life will create two mirrored Sierpiński triangles. The time-space diagram of a replicator pattern in a cellular automaton also often resembles a
Sierpiński_triangle
American computer scientist
and Michael A. Harrison in context-sensitive parsing using the stack automaton model. Besides establishing the normal form (Greibach normal form) for
Sheila_Greibach
2026 video game
We ask the devs about Leon's role and "RE4-style" battle mechanics". Automaton (Interview). Retrieved December 12, 2025. Zachary, Brandon (January 28
Resident_Evil_Requiem
Subfield of computer science and mathematics
back to the 1960s, states that the entire universe is a huge cellular automaton which continuously updates its rules. Recently it has been suggested that
Theoretical_computer_science
Mathematical model for sequential decision making under uncertainty
such an automaton correspond to the states of a "discrete-state discrete-parameter Markov process". At each time step t = 0,1,2,3,..., the automaton reads
Markov_decision_process
On linear-time algorithms for graph logic
the construction of a finite bottom-up tree automaton that acts on the tree decompositions of the given graph. In more detail, two graphs G1 and G2, each
Courcelle's_theorem
Open-source library for pattern matching in text
typos of the "swap" type (see Damerau–Levenshtein distance). Levenshtein automaton Comparison of regular expression engines Agrep "R: Pattern Matching for
TRE_(computing)
Ability of a computing system to simulate Turing machines
a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can
Turing_completeness
Abstract machine used in a formal logic and theoretical computer science
A counter machine or counter automaton is an abstract machine used in a formal logic and theoretical computer science to model computation. It is the
Counter_machine
Grammar formalism
languages that TAGs can generate may be represented by an embedded pushdown automaton. Tree-adjoining grammars are often described as mildly context-sensitive
Tree-adjoining_grammar
Set of infinite words
considered synonyms. The most widely studied shift spaces are the subshifts of finite type and the sofic shifts. In the classical framework a shift space is any
Shift_space
Mathematical model of abstract computation
arbitrary finite computations. He then employed a novel approach to extend that construction to unbounded computations. The proof proceeds in two stages
Wolfram's 2-state 3-symbol Turing machine
Wolfram's_2-state_3-symbol_Turing_machine
Deterministic model of computation
called the deletion number. A is a finite alphabet of symbols, one of which can be a special halting symbol. All finite (possibly empty) strings on A are
Tag_system
Random process independent of past history
in the setting with finite state space. In a more abstract way, Markov processes can also be defined or constructed the other way around: Let ( P t )
Markov_chain
2021 video game
Metroidvania adventure game in which players assume the role of Alma, an automaton who has amnesia in the aftermath of a war between humans and robots. In
Unsighted
Algebraic structure
for any automaton or finite-state machine (FSM). The bicyclic semigroup is in fact a monoid, which can be described as the free semigroup on two generators
Semigroup
Functional programming construct
other pattern languages include unique or unusual extensions. Binding A way of associating a name with a portion of the scrutinee, so that the name is
Pattern_matching
Type of parser in computer science
if we are considering a finite automaton that can read terminals as well as nonterminals. The begin state of this automaton is always the closure of
LR_parser
Emptiness problem for a nondeterministic two-way finite state automaton Equivalence problem for nondeterministic finite automata Word problem and emptiness
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
English mathematician (1937–2020)
recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the
John_Horton_Conway
Mathematical conjecture
In computer science, more precisely, in the theory of deterministic finite automata (DFA), a synchronizing word or reset sequence is a word in the input
Synchronizing_word
Computer science metric of string similarity
called the pattern, and a constant k; it then builds a deterministic finite state automaton that finds, in an arbitrary string s, a substring whose edit distance
Edit_distance
Finite-state machine whose output values are determined only by its current state
In the theory of computation, a Moore machine is a finite-state machine whose current output values are determined only by its current state. This is in
Moore_machine
2D cellular automaton similar to Conway's Game of Life
cellular automaton is a type of model studied in mathematics and theoretical biology consisting of a regular grid of cells, each in one of a finite number
Life_without_Death
Hardware cache of a central processing unit
to index a way in the set. For example, in a 4-way set associative cache, the two bits are used to index way 00, way 01, way 10, and way 11, respectively
CPU_cache
Computer science field
model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness)
Model_checking
Algorithmic problem on pairs of sequences
longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring: unlike substrings
Longest_common_subsequence
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TWO WAY-FINITE-AUTOMATON
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