Powerset construction, Theory of Computation

Assignment Help:

As de?ned the powerset construction builds a DFA with many states that can never be reached from Q′0. Since they cannot be reached from Q′0 there is no path from Q′0 to a state in F′ which passes through them and they can be deleted from the automaton without changing the language it accepts. In practice it is much easier to build Q′ as needed, only including those state sets that actually are needed.

To see how this works, lets carry out an example. For maximum generality, let's start with the NFA with ε-transitions given above, repeated here:

1876_Powerset Construction.png

Because it is simpler to write the transition function (δ) out as a table than it is to write out the transition relation (T) as a set of tuples, we will work with the δ representation. When given a transition graph of an NFA with ε-transitions like this there are 6 steps required to reduce it to a DFA:

1. Write out the transition function and set of ?nal states of the NFA.

2. Convert it to an NFA without ε-transitions.

(a) Compute the ε-Closure of each state in the NFA.

(b) Compute the transition function of the equivalent NFA without ε-transitions.

(c) Compute the set of ?nal states of the equivalent NFA without ε- transitions.


Related Discussions:- Powerset construction

Two-tape turing machine, Let there L1 and L2 . We show that L1 ∩ L2 is CFG ...

Let there L1 and L2 . We show that L1 ∩ L2 is CFG . Let M1 be a decider for L1 and M2 be a decider for L2 . Consider a 2-tape TM M: "On input x: 1. copy x on the second

Finite automata, design an automata for strings having exactly four 1''s

design an automata for strings having exactly four 1''s

Programming languages, Different types of applications and numerous program...

Different types of applications and numerous programming languages have been developed to make easy the task of writing programs. The assortment of programming languages shows, dif

Design and implementation of the state machine, You are required to design ...

You are required to design a system that controls the speed of a fan's rotation. The speed at which the fan rotates is determined by the ambient temperature, i.e. as the temperatur

Project, can you plz help with some project ideas relatede to DFA or NFA or...

can you plz help with some project ideas relatede to DFA or NFA or anything

Closure properties to prove regularity, The fact that regular languages are...

The fact that regular languages are closed under Boolean operations simpli?es the process of establishing regularity of languages; in essence we can augment the regular operations

Possibility of recognizing the palindrome language, Computer has a single F...

Computer has a single FIFO queue of ?xed precision unsigned integers with the length of the queue unbounded. You can use access methods similar to those in the third model. In this

Prism algorithm, what exactly is this and how is it implemented and how to ...

what exactly is this and how is it implemented and how to prove its correctness, completeness...

Union, Intuitively, closure of SL 2 under intersection is reasonably easy ...

Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd