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Automata), finite automaton, or simply a state machine, is a mathematical model of computation If, and only if, the resulting automata agree up to renaming of states, the regular expressions' languages agree. [1] it is an abstract machine that can be in exactly one of a finite number of states at any given time.

The figure illustrates a deterministic finite automaton using a state diagram To decide whether two given regular expressions describe the same language, each can be converted into an equivalent minimal deterministic finite automaton via thompson's construction, powerset construction, and dfa minimization In this example automaton, there are three states

S 0, s 1, and s 2 (denoted graphically by circles)

The automaton takes a finite sequence of 0s and 1s as input For each state, there is a transition arrow leading out to a next state for both 0 and 1. A classic form of state diagram for a finite automaton (fa) is a directed graph with the following elements (q, σ, z, δ, q 0, f) A finite set of states, normally represented by circles and labeled with unique designator symbols or words written inside them input symbols σ

A finite collection of input symbols or designators The automaton described by this state diagram starts in state s 1, and changes states following the arrows marked 0 or 1 according to the input symbols as they arrive The double circle marks s 1 as an accepting state Since all paths from s 1 to itself contain an even number of arrows marked 0, this automaton accepts strings containing even numbers of 0s

Automata theory is the study of.

In this kind of automaton, the transition function is additionally defined on the empty string ε. Weighted automaton hasse diagram of some classes of quantitative automata, ordered by expressiveness A finite set of states a start state (also called initial state) which is an element of a finite set called the input alphabet a finite set called the output alphabet a transition function mapping a state and the input alphabet to the next state an output function mapping each state to the output alphabet evolution.

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