Finite State Automata That Accepts Any String

The other state, the one for having seen an odd number of as, is an accept state. Introduction to Automata Theory. Hopcroft, Rajeev Motwani, Jeffrey D. Finite Automata (FA) (Based on John E.

Unfortunately, that DFA also accepts b, so we cant use that. We will need at least one state to remember the empty string (and strings like it - strings to which we can append the empty string or any other string in the language and still have a string in the language) this will be the start/initial state, and since the empty string is in the language (we check this easily), we know the start/initial state will be accepting.There is a DFA that accepts a (among other things) which has one state: the one-state DFA that accepts every string. Additionally, we can append any string in the language we are going for to the empty string, and we will get a string in the language (trivially). What can you append to this to get a string in the language? Well, the empty string is in the language, so we can append the empty string (i.e., nothing) and also have a string in the language. However, we can also add an a followed by any string in the language, and get another string in the language.Computer Science: Deterministic finite automata that accepts the only the string 'aabb'Helpful Please support me on Patreon: you start with the empty string. We can also trivially add any other string in the language to the end of this string, and get another string in the language.

You should find that the strings aa and ab are both already covered by our dead state (we can't add any strings to the end of these to get anything in our language), and that the string ba is covered by the start/initial state (we can only add to this strings already in the language to get other strings in the language), and that bb corresponds to the third state we identified (adding any string, or a single a followed by any string, will result in a string also in the language). It will be accepting, since the string b is a string in the language.You should try the strings aa, ab, ba, and bb. The set of strings which we can add is therefore a set we haven't seen before, and we will need a new state to represent this string - the string b - and strings like it. For instance, we can add the string a followed by bbabb to get babbabb, which is also in the language. However, we can also add an a followed by any string in the language, and get another string in the language.

The other transitions are found similarly: on either an a or a b, the dead state transitions to itself, and the third state loops on b and transitions to the start/initial state on an a. Similarly, we need a transition from the start/initial state to the third state on the symbol b. In other words, since the string a is formed by adding the character a to the end of the empty string, we need a transition from the start/initial state (corresponding to the empty string) to the dead state (corresponding to the string a) which occurs when the FA reads the symbol a.

Which is a nice way to solve problems requesting one, instead of coming up with an arbitrary one and minimizing it post-hoc. Moreoever, by constructing it in this fashion, you guarantee that you have a minimal FA.

Finite State Automata That Accepts Any String