Emptiness problem, Theory of Computation

Assignment Help:

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.

Proof: We'll sketch three different algorithms for deciding the Emptiness Problem, given some DFA A = (Q,Σ, T, q0, F).

(Emptiness 1) A string w is in L(A) iff it labels a path through the transition graph of A from q0 to an accepting state. Thus, the language will be non-empty iff there is some such path. So the question of Emptiness reduces to the question of connectivity: the language recognized by A is empty iff there is no accepting state in the connected component of its transition graph that is rooted at q0. The problem of determining connected components of directed graphs is algorithmically solvable,by Depth-First Search, for instance (and solvable in time linear in the number of nodes). So, given A, we just do a depth-?rst search of the transition graph rooted at the start state keeping track of whether we encounter any accepting state. We return "True" iff we ?nd none.


Related Discussions:- Emptiness problem

TRANSPORTATION, DEGENERATE OF THE INITIAL SOLUTION

DEGENERATE OF THE INITIAL SOLUTION

Operations on strictly local languages, The class of Strictly Local Languag...

The class of Strictly Local Languages (in general) is closed under • intersection but is not closed under • union • complement • concatenation • Kleene- and positive

How to solve the checking problem, The objective of the remainder of this a...

The objective of the remainder of this assignment is to get you thinking about the problem of recognizing strings given various restrictions to your model of computation. We will w

Sketch an algorithm to recognize the language, First model: Computer has a ...

First model: Computer has a ?xed number of bits of storage. You will model this by limiting your program to a single ?xed-precision unsigned integer variable, e.g., a single one-by

Applying the pumping lemma, Applying the pumping lemma is not fundamentally...

Applying the pumping lemma is not fundamentally di?erent than applying (general) su?x substitution closure or the non-counting property. The pumping lemma is a little more complica

Non - sl languages, Application of the general suffix substitution closure ...

Application of the general suffix substitution closure theorem is slightly more complicated than application of the specific k-local versions. In the specific versions, all we had

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

Closure properties of recognizable languages, We got the class LT by taking...

We got the class LT by taking the class SL and closing it under Boolean operations. We have observed that LT ⊆ Recog, so certainly any Boolean combination of LT languages will also

Notes, write short notes on decidable and solvable problem

write short notes on decidable and solvable problem

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