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

Equivalence of nfas and dfas, In general non-determinism, by introducing a ...

In general non-determinism, by introducing a degree of parallelism, may increase the accepting power of a model of computation. But if we subject NFAs to the same sort of analysis

Equivalence of nfas, It is not hard to see that ε-transitions do not add to...

It is not hard to see that ε-transitions do not add to the accepting power of the model. The underlying idea is that whenever an ID (q, σ  v) directly computes another (p, v) via

Designing finite automata, a finite automata accepting strings over {a,b} e...

a finite automata accepting strings over {a,b} ending in abbbba

Ogdens lemma, proof ogdens lemma .with example i am not able to undestand ...

proof ogdens lemma .with example i am not able to undestand the meaning of distinguished position .

Answer, And what this money. Invovle who it involves and the fact of,how we...

And what this money. Invovle who it involves and the fact of,how we got itself identified candidate and not withstanding time date location. That shouts me media And answers who''v

Finite-state automaton, Paths leading to regions B, C and E are paths which...

Paths leading to regions B, C and E are paths which have not yet seen aa. Those leading to region B and E end in a, with those leading to E having seen ba and those leading to B no

Pushdown automator, draw pda for l={an,bm,an/m,n>=0} n is in superscript

draw pda for l={an,bm,an/m,n>=0} n is in superscript

Qbasic, Ask question #Minimum 100 words accepte

Ask question #Minimum 100 words accepte

#dfa, Give DFA''s accepting the following languages over the alphabet {0,1}...

Give DFA''s accepting the following languages over the alphabet {0,1}: i. The set of all strings beginning with a 1 that, when interpreted as a binary integer, is a multiple of 5.

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