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

what is a turing machine, A Turing machine is a theoretical computing mach...

A Turing machine is a theoretical computing machine made-up by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine having of a line of

Universality problem, The Universality Problem is the dual of the emptiness...

The Universality Problem is the dual of the emptiness problem: is L(A) = Σ∗? It can be solved by minor variations of any one of the algorithms for Emptiness or (with a little le

Turing machine, Can v find the given number is palindrome or not using turi...

Can v find the given number is palindrome or not using turing machine

Myhill graph of the automaton, Exercise:  Give a construction that converts...

Exercise:  Give a construction that converts a strictly 2-local automaton for a language L into one that recognizes the language L r . Justify the correctness of your construction.

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

what are the advantages and disadvantages of wearable computers?

Abstract model of computation, When we say "solved algorithmically" we are ...

When we say "solved algorithmically" we are not asking about a speci?c programming language, in fact one of the theorems in computability is that essentially all reasonable program

Non - sl languages, The key thing about the Suffx Substitution Closure prop...

The key thing about the Suffx Substitution Closure property is that it does not make any explicit reference to the automaton that recognizes the language. While the argument tha

Data retriving, i have research method project and i meef to make prposal w...

i have research method project and i meef to make prposal with topic. If this service here please help me

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

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