1.Construct an NFA accepting L given by {x|(a,b)*|,|x|>=3 and the third symbol of x from the right is 'b'?
2.construct an NFA for the regular expression r=1*0+0?
3.construct an NFA to accept the language indicated by the following regular expression ((01+001)*0*)
4.construct a nfa accepting the same of strings over{a,b} ending in aba .Use it to construct a DFA accepting the same set of strings ?
5.construct transition diagram of a finite automata corresponding to the regular expression (a b+c*)*b?
6.prove that there is no string in(a,b)* such that ax=xb
7.construct an NFA equivalent to the regular expression ((10)+(0+1))*01?
8.show that the language{ 0^n 1^n 2^n /n>=1}is not a context free?
please get me a answer for these questions

Hi
The objectives for studying the theory of computation are analogous to those for studying physics. For example, physics helps explain the possibilities and limitations of the physical world we live in. In a similar manner, the theory of computation helps explain the possibilities and limitations of computers, both physical and virtual. Just as the engineering of physical systems must consult physics for the needed scientific principles, so must the engineering of computing and information systems consult the theory of computation.