Question

What is the language recognized by the automaton in Exercise \(19\)\(?\)

Short answer

The language recognized by the automaton is the empty set \(\emptyset \)

Step-by-step solution

Definition

A finite-state automaton \(M = \left( {S,I,f,{s_0},F} \right)\) consists of a finite set S of states, a finite input alphabet I, a transition function f that assigns a next state to every pair of state and input (so that \(f:S \times I \to S\)), an initial or start state \({s_0}\), and a subset F of S consisting of final (or accepting states).

Finding the language recognized by the automaton

You note that the given automaton contains no final states, because there is no state \({s_i}\) that is encased within 2 circles.

Since the deterministic finite-state automaton contains no final states, no strings will be recognized by the language.

Therefore, the language recognized by the automaton is the empty set \(\emptyset \).