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

Decision problems of regular languages, We'll close our consideration of re...

We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.

Give a strictly 2-local automaton, Let L 3 = {a i bc j | i, j ≥ 0}. Give ...

Let L 3 = {a i bc j | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L 3 . Use the construction of the proof to extend the automaton to one that recognizes L 3 . Gi

Myhill graphs, Another way of representing a strictly 2-local automaton is ...

Another way of representing a strictly 2-local automaton is with a Myhill graph. These are directed graphs in which the vertices are labeled with symbols from the input alphabet of

Prove the arden''s theorem, State and Prove the Arden's theorem for Regular...

State and Prove the Arden's theorem for Regular Expression

Transition and path functions, When an FSA is deterministic the set of trip...

When an FSA is deterministic the set of triples encoding its edges represents a relation that is functional in its ?rst and third components: for every q and σ there is exactly one

Production, How useful is production function in production planning?

How useful is production function in production planning?

Convert chomsky normal form into binary form, Suppose G = (N, Σ, P, S) is a...

Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the

Computations of sl automata, We will specify a computation of one of these ...

We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea

Myhill-nerode, Theorem (Myhill-Nerode) A language L ⊆ Σ is recognizable iff...

Theorem (Myhill-Nerode) A language L ⊆ Σ is recognizable iff ≡L partitions Σ* into ?nitely many Nerode equivalence classes. Proof: For the "only if" direction (that every recogn

Non Regular, Prove that Language is non regular TRailing count={aa ba aaaa...

Prove that Language is non regular TRailing count={aa ba aaaa abaa baaa bbaa aaaaaa aabaaa abaaaa..... 1) Pumping Lemma 2)Myhill nerode

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