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

Equivalence problem, The Equivalence Problem is the question of whether two...

The Equivalence Problem is the question of whether two languages are equal (in the sense of being the same set of strings). An instance is a pair of ?nite speci?cations of regular

Automata, As we are primarily concerned with questions of what is and what ...

As we are primarily concerned with questions of what is and what is not computable relative to some particular model of computation, we will usually base our explorations of langua

Defining strictly local automata, One of the first issues to resolve, when ...

One of the first issues to resolve, when exploring any mechanism for defining languages is the question of how to go about constructing instances of the mechanism which define part

Generalization of the interpretation of local automata, The generalization ...

The generalization of the interpretation of strictly local automata as generators is similar, in some respects, to the generalization of Myhill graphs. Again, the set of possible s

Wearable computers.., what are the advantages and disadvantages of wearable...

what are the advantages and disadvantages of wearable computers?

#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.

Class of local languages is not closed under union, Both L 1 and L 2 are ...

Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con

Brain game, If the first three words are the boys down,what are the last th...

If the first three words are the boys down,what are the last three words??

Prepare the consolidated financial statements, Prepare the consolidated fin...

Prepare the consolidated financial statements for the year ended 30 June 2011. On 1 July 2006, Mark Ltd acquired all the share capitall of john Ltd for $700,000. At the date , J

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

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