Automata Theory + Help plz

[Guest nivsah]

1. construct DFA's for the following language

 

a, The set of binary strings beginning with 010 and ending with 100

 

b, the set of string over {0,1_ which do not contain 0110 as substring

 

c, the set of strings over {a,b} such that the fifth symbol from the right is a

 

d, the set of binary strings containing at least two 1's and most three 0's

 

2. for any language L let L1/3,* be the set of all first thirs of strings in L i.e,

L1/3,* = {x | Ey : |y| = 2|X|,xy E L}. show that L is regular, then so is L1/3,*.