Design Finite Automata

Problem 1: For languages L1 to L10 over alphabets {a,b} do the following a) Enumerate some elements b) Draw a Deterministic Finite Automata  L1: The language of all strings containing even number of a’s and each a is followed by at least one b.  L2:The language that has even length and odd number of a’s.  L3:The language of all strings in which every pair of adjacent b’s appear before any pair of adjacent a’s.  L4:The language of all strings containing no more than one occurrence of the string aa. (the string aaa should be viewed as containing 2 occurrences of aa)  L6: The language of all strings that begins and end with a triple letter( aaa or bbb)  L7: The language of all strings containing at least two a’s and at most one b. Problem 2a: For languages L1 to L10 over alphabets {0,1} do the following a) Enumerate some elements b) Draw a Deterministic Finite Automata  L1: strings over {0,1} such that their decimal equivalent is multiple of 5 Eg: {0, 101,1010…..}  L2: all strings over {0,1} that start with 0 and end with 010 and do not have 000 as part of a string.  L3: all the string x in which n 0 (x)%3=0 and n 1 (x)%3!=0  L4: all the string x in which n 0 (x)%3=0 and n 1 (x)%3=0  L5: L4 U L3  L6= L1’ School of Computer SciencePage2 Problem 2a: Run DFA of L1 of problem 2 for following strings, and answer which ones are accepted and which are rejected {000111, 101000, 10110100,0000100000}