Deterministic automaton

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Deterministic automaton is a concept of automata theory in which the outcome of a transition from one state to another given a certain input can be predicted for every occurrence.

A common deterministic automaton is a deterministic finite automaton (DFA)) which is a finite state machine where for each pair of state and input symbol there is one and only one transition to a next state. DFAs recognize the set of regular languages and no other languages.

The standard way to build a deterministic finite automaton from a nondeterministic finite automaton is the powerset construction.

Automata theory: formal languages and formal grammars

Chomsky hierarchy	Grammars	Languages	Abstract machines
Type-0 — Type-1 — — — — — Type-2 — — Type-3 — —	Unrestricted (no common name) Context-sensitive Positive range concatenation Indexed — Linear context-free rewriting systems Tree-adjoining Context-free Deterministic context-free Visibly pushdown Regular — Non-recursive	Recursively enumerable Decidable Context-sensitive Positive range concatenation^* Indexed^* — Linear context-free rewriting language Tree-adjoining Context-free Deterministic context-free Visibly pushdown Regular Star-free Finite	Turing machine Decider Linear-bounded PTIME Turing Machine Nested stack Thread automaton restricted Tree stack automaton Embedded pushdown Nondeterministic pushdown Deterministic pushdown Visibly pushdown Finite Counter-free (with aperiodic finite monoid) Acyclic finite

Each category of languages, except those marked by a ^*, is a proper subset of the category directly above it. Any language in each category is generated by a grammar and by an automaton in the category in the same line.

P ≟ NP

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