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**Finite Automata:**

A finite-state machine (FSM) or finite-state automaton (plural: automata), or just a state machine, is a mathematical model of computation used to design computer programs and sequential logic circuits both. It is conceived as an abstract machine that can be in one of a finite number of states. The machine is in just one state at a time; the state it is in at any given time is called the current state. It can modify from one state to another while initiated by a triggering event or condition; it is called a transition. A particular FSM is described by a list of its states, and the triggering condition for each of the transition.

Finite-state machines can model a great number of troubles, among which are electronic design automation, language parsing, communication protocol design, and other engineering applications. In artificial intelligence and biology research, state machines or hierarchies of state machines have been used to describe neurological systems and in linguistics—to describe the grammars of natural languages.

**Types of Finite Automata:**

Deterministic Finite Automata (DFA):

The machine can stay in only y g y one state at any given time.

A DFA is described by the 5-tuple:

{Q, ∑, q_{o}, F, δ}

Where,

Q = a finite set of states

∑ = a finite set of input symbols (alphabet)

q_{0} = a start state

F = set of final states

δ = a transition function, which is a mapping between Q x ∑ = Q

Non-deterministic Finite Automata (NFA):

The machine can stay in multiple states at the similar time. Outgoing transitions could be non-deterministic.

An NFA is also described by the 5-tuple:

{Q, ∑, q_{o}, F, δ}

Where,

Q = a finite set of states

∑ = a finite set of input symbols (alphabet)

q_{0} = a start state

F = set of final states

δ = a transition function, which is a mapping between Q x ∑ = subset of Q

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