Finite Automaton: Accessibility of String

Acceptability of String

A string ‘w’ is accepted by finite automaton ‘M’ if δ(q0, w) -> q, for some q belongs to F.  or we can write; The string is said to be accepted by finite automaton if.

L= {w | δ (q0, w) is in F}

Here δ (q0, w) is a resulting state when a finite automaton reads ‘w’ i.e. a string one alphabet symbol at a time, and goes to a state which is a final state.

Language of FA

Given δ(q0,w) -> q, it means after reading string ‘w’ symbol by symbol ( one symbol at a time) machine reaches to q state. If this q state is the final state i.e. q ∈ F then ‘w’ is said to be accepted else if p ∉ F, then ‘w’ is said to be rejected.

If there is a language L such that

          L={w  | δ(q0, w) is in F} then it is said to be accepted by the finite automata M and denoted by L(M).

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