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

Finite state automata, Since the signi?cance of the states represented by t...

Since the signi?cance of the states represented by the nodes of these transition graphs is arbitrary, we will allow ourselves to use any ?nite set (such as {A,B,C,D,E, F,G,H} or ev

Kleene closure, One might assume that non-closure under concatenation would...

One might assume that non-closure under concatenation would imply non closure under both Kleene- and positive closure, since the concatenation of a language with itself is included

Nfas with e-transitions, We now add an additional degree of non-determinism...

We now add an additional degree of non-determinism and allow transitions that can be taken independent of the input-ε-transitions. Here whenever the automaton is in state 1

Emptiness problem, The Emptiness Problem is the problem of deciding if a gi...

The Emptiness Problem is the problem of deciding if a given regular language is empty (= ∅). Theorem 4 (Emptiness) The Emptiness Problem for Regular Languages is decidable. P

Recognition problem, The Recognition Problem for a class of languages is th...

The Recognition Problem for a class of languages is the question of whether a given string is a member of a given language. An instance consists of a string and a (?nite) speci?cat

Formal language theory, This was one of the ?rst substantial theorems of Fo...

This was one of the ?rst substantial theorems of Formal Language Theory. It's maybe not too surprising to us, as we have already seen a similar equivalence between LTO and SF. But

Automata, how to prove he extended transition function is derived from part...

how to prove he extended transition function is derived from part 2 and 3

Automata answer, build a TM that enumerate even set of even length string o...

build a TM that enumerate even set of even length string over 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