# Automata theory

**automataautomatonautomata theoriestheory of automataanalog automataautomata evolutioncomputational automatafinite automataword**

Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.wikipedia

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### Abstract machine

**abstract computerabstract computer modelcomputational models**

Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.

An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in automata theory.

### Theoretical computer science

**theoretical computer scientisttheoreticalcomputer science**

It is a theory in theoretical computer science and discrete mathematics (a subject of study in both mathematics and computer science).

Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.

### State (computer science)

**statestatefulstates**

This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows).

Examples of such systems are digital logic circuits and components, automata and formal language, computer programs, and computers.

### Discrete mathematics

**discretediscrete mathdiscrete structure**

It is a theory in theoretical computer science and discrete mathematics (a subject of study in both mathematics and computer science).

Automata theory and formal language theory are closely related to computability.

### Theory of computation

**computational theoristcomputational theorycomputation theory**

Automata play a major role in theory of computation, compiler construction, artificial intelligence, parsing and formal verification.

The field is divided into three major branches: automata theory and languages, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?".

### Formal language

**formal language theoryformal languageslanguage**

Automata theory is closely related to formal language theory.

Formal languages may be classified in the Chomsky hierarchy based on the expressive power of their generative grammar as well as the complexity of their recognizing automaton.

### Computer science

**computer scientistcomputer sciencescomputer scientists**

It is a theory in theoretical computer science and discrete mathematics (a subject of study in both mathematics and computer science).

Formal methods are best described as the application of a fairly broad variety of theoretical computer science fundamentals, in particular logic calculi, formal languages, automata theory, and program semantics, but also type systems and algebraic data types to problems in software and hardware specification and verification.

### Alternating finite automaton

**alternating automataalternatingAlternating automaton**

### Pushdown automaton

**pushdown automataNondeterministic pushdown automatonPush-Down Automaton**

In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack.

### DFA minimization

**minimal automatonminimizedBrzozowski's algorithm for DFA minimization**

In automata theory (a branch of theoretical computer science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states.

### Alphabet (formal languages)

**alphabetalphabetsinput symbol**

An automaton processes one input picked from a set of symbols or letters, which is called an alphabet.

Alphabets are important in the use of formal languages, automata and semiautomata.

### Deterministic automaton

**deterministicdeterministicallynon-deterministic**

In computer science, a deterministic automaton is a concept of automata theory in which the outcome of a transition from one state to another is determined by the input.

### Deterministic pushdown automaton

**deterministic pushdown automatapush-down store**

In automata theory, a deterministic pushdown automaton (DPDA or DPA) is a variation of the pushdown automaton.

### Automaton

**automataautomaticautomatons**

Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.

### Büchi automaton

**Büchi automataclosure properties of Büchi automata**

In computer science and automata theory, a Büchi automaton is a type of ω-automaton, which extends a finite automaton to infinite inputs.

### Ω-automaton

**Rabin automatonω-automataRabin Automata**

In automata theory, a branch of theoretical computer science, an ω-automaton (or stream automaton) is a variation of finite automatons that runs on infinite, rather than finite, strings as input.

### Tree (automata theory)

**treestreetree of symbols**

For example, each node of the tree is a word over set of natural numbers, which helps this definition to be used in automata theory.

### Muller automaton

**Muller automataMuller**

In automata theory, a Muller automaton is a type of an ω-automaton.

### Nondeterministic finite automaton

**nondeterministic finite automataNFAnondeterministic machine**

For a more elementary introduction of the formal definition see automata theory.

### Hybrid automaton

**hybrid automatahybrid discrete-continuous automata**

Normally automata theory describes the states of abstract machines but there are analog automata or continuous automata or hybrid discrete-continuous automata, which use analog data, continuous time, or both.

In automata theory, a hybrid automaton (plural: hybrid automata or hybrid automatons) is a mathematical model for precisely describing systems in which digital computational processes interact with analog physical processes.

### Finite-state machine

**finite state machinestate machinefinite automata**

The figure at right illustrates a finite-state machine, which belongs to a well-known type of automaton.

FSMs are studied in the more general field of automata theory.

### Deterministic finite automaton

**deterministic finite automataDFAdeterministic finite state automaton**

The most standard variant, which is described above, is called a deterministic finite automaton.

For more comprehensive introduction of the formal definition see automata theory.

### Monoid

**commutative monoidmonoidsmonoid homomorphism**

Monoids are also considered as a suitable setting for automata in monoidal categories.

In theoretical computer science, the study of monoids is fundamental for automata theory (Krohn–Rhodes theory), and formal language theory (star height problem).

### Boolean differential calculus

**boolean derivativeboolean differencePotential variable (Boolean differential calculus)**

* Boolean differential calculus

### Computational problem

**computational problemsproblemdecision problem**