Finite state automata accept both 00 and 11

For the rest, just figure out what string you'd get by adding to the canonical one, and which class the resulting string would be in. So we have four states - let's call them, ,, and. If you try all strings of length 3, you will find that all of those already fall into one of the above classes, and you can stop checking at that point. The string 11 ends up being in the same class as the empty string: you can add any string in the language to 11 and get another string in the language. It turns out that the next strings, 01 and 10, are also in this class. What about the string 00? This string is not in the language, and no other string can be added to this string to get a string in the language. What about the string 1? It's distinguishable from both 0 and the empty string, since you can add 10 to 1 to get 110, a string in the language, but you can't add it to 0 or the empty string to get a string in the language. Both of these will need different states in our FA. We have found two distinct equivalence classes so far - one for the empty string, one for 0. In the case of the finite automata shown in figure 1, the following points may be noted: (i) On input 0 in state q0, the next state may be either of the two. Give a NFA that only accepts binary numbers that include both 00 and 11. A two-way nondeterministic finite automaton (2NFA) may have multiple transitions defined in the same configuration. Two-way nondeterministic finite automaton.

The string 0 is in a different equivalent class, since you can add the empty string to 0 and get a string in the language (whereas you can't add the empty string to the empty string to get a string in the language). How long could it take to reduce a NFA with n states and t transitions to a. It says that once the automaton reaches the accept or reject state, it stays in there forever and the pointer goes to the right most symbol and cycles there infinitely. The empty string is in some equivalence class. In your case, let's try to identify equivalence classes. Two strings x and y are indistinguishable, in this sense, if for any other string z, either both xz and yz are in the language, or neither is. The Myhill-Nerode theorem allows you to find the necessary (and sufficient!) states of for a finite automaton if you are able to identify the equivalence classes of 'indistinguishable' strings. To construct a finite automaton, you need to identify the states and transitions. Should I include 0 as a string from this set?

Finite state automata accept both 00 and 11