DFA simulating NFA: the power set construction

Theorem (equivalence NFA-DFA): Any NFA N can be transformed to an equivalent DFA M.

Proof: Thanks to Lemma on ε-transitions, assume with no loss of generality which N = (S, A, f, s0, F) consists of no ε-transitions. Define M = (2S, A, f’, {s0}, F’) as follows. 2S is the power set of S, {s0} the initial state. F’ comprises of all such subsets R ⊆ S which have some final state of N that s, R ∩ F ≠ {}. f’:  2S x A  -> 2S is defined as:

For R ∈ 2S and a ∈ A, f’(R, a) = {s ∈ S | s ∈ f(r, a) for some r ∈ R}.

N and M are equal due the given invariant: for all x ∈ A*, f’({s0}, x) = f(s0, x). QED

Illustration: Convert the NFA N converted to an ε-free NFA M. E(s1) = {s1, s3}.  L = (a ∪ ba* (a ∪ b) a)* to an equivalent DFA

The power set construction tends to introduce the unreachable states. Such can be removed by using a transitive closure algorithm. Alternatively, we make states of M only as the corresponding subsets of S are being reached, therefore joining transitive closure with the construction of state space. For simplicity of comparison, let’s redraw the DFA above with no unreachable states, with a layout identical to illustration above. The non-determinism in illustration above: f(s2, a) = {s2, s3} is resolved by introducing the states {s2, s3} and {s1, s2, s3}:

Latest technology based Theory of Computation Online Tutoring Assistance

Tutors, at the www.tutorsglobe.com, take pledge to provide full satisfaction and assurance in Theory of Computation help via online tutoring. Students are getting 100% satisfaction by online tutors across the globe. Here you can get homework help for Theory of Computation, project ideas and tutorials. We provide email based Theory of Computation help. You can join us to ask queries 24x7 with live, experienced and qualified online tutors specialized in Theory of Computation. Through Online Tutoring, you would be able to complete your homework or assignments at your home. Tutors at the TutorsGlobe are committed to provide the best quality online tutoring assistance for Theory of Computation Homework help and assignment help services. They use their experience, as they have solved thousands of the Theory of Computation assignments, which may help you to solve your complex issues of Theory of Computation. TutorsGlobe assure for the best quality compliance to your homework. Compromise with quality is not in our dictionary. If we feel that we are not able to provide the homework help as per the deadline or given instruction by the student, we refund the money of the student without any delay.