9 Informal Description of M 5 M 5 keeps a running count of the sum of the numerical symbols it reads, modulo 3. Every time it receives the symbol it resets the count to 0. M 5 accepts if the sum is 0, modulo 3.
10 Definition 1.7: Regular Language A language is called a regular language if some finite automaton recognizes it.
11 Example 1.9: A finite automaton E 2 E 2 recognizes the regular language of all strings that contain the string 001 as a substring. 0010, 1001, 001, and 1111110011110 are all accepted, but 11 and 0000 are not.
12 Find a set of states of E 2 You 1.haven’t just seen any symbols of the pattern, 2.have just seen a 0, 3.have just seen 00 or, 4.have just seen the entire pattern 001. Assign the states q,q 0,q 00, and q 001 to these possibilities.
13 Draw a State Diagram for E 2 q 00 q 001 0 0, 1 1 1 0 q0q0 0 q 1
Proof of Th 1.1219 Correctness You should check the following. 1.For any string recognized by M 1 is recognized by M. 2.For any string recognized by M 2 is recognized by M. 3.For any string recognized by M is recognized by M 1 or M 2.
21 Nondeterminism To prove Theorem 1.13, we need nondeterminism. Nondeterminism is a generalization of determinism. So, every deterministic automaton is automatically a nondeterministic automaton.
22 Nondetermistic Finite Automata A nondeterministic finite automaton can be different from a deterministic one in that –for any input symbol, nondeterministic one can transit to more than one states. –epsilon transition NFA and DFA stand for nondeterministic finite automaton and deterministic finite automaton, respectively.