Recognizable languages The recognizable languages are the set of languages that are recognized by some automaton. The language L ⊆ Σ* recognized by an automaton is the set of all the words that are accepted by the automaton. Recognized language An automaton can recognize a formal language. Accepting word A word w ∈ Σ* is accepted by the automaton if q n ∈ F. q n is said to be the final state of the run. When the automaton reads symbol a i it jumps to state q i = δ(q i-1,a i). In other words, at first the automaton is at the start state q 0, and then the automaton reads symbols of the input word in sequence. Run A sequence of states q 0,q 1,q 2., q n, where q i ∈ Q such that q 0 is the start state and q i = δ(q i-1,a i) for 0 < i ≤ n, is a run of the automaton on an input word w = a 1,a 2., a n ∈ Σ*. Input word An automaton reads a finite string of symbols a 1,a 2., a n, where a i ∈ Σ, which is called an input word. q 0 is the start state, that is, the state of the automaton before any input has been processed, where q 0∈ Q.δ is the transition function, that is, δ: Q × Σ → Q.Σ is a finite set of symbols, called the alphabet of the automaton. Formal definitionĪ deterministic finite automaton is represented formally by a 5-tuple, where: An automaton is a construct made of states which designed to determine if the input should be accepted or rejected.
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