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

Computation of an automaton, The computation of an SL 2 automaton A = ( Σ,...

The computation of an SL 2 automaton A = ( Σ, T) on a string w is the maximal sequence of IDs in which each sequential pair of IDs is related by |- A and which starts with the in

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

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

Mapping reducibility, Can you say that B is decidable? If you somehow know...

Can you say that B is decidable? If you somehow know that A is decidable, what can you say about B?

#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.

Computer Simulation, Generate 100 random numbers with the exponential distr...

Generate 100 random numbers with the exponential distribution lambda=5.0.What is the probability that the largest of them is less than 1.0?

What is pumping lemma for regular sets, State & prove pumping lemma for reg...

State & prove pumping lemma for regular set. Show that for the language L={ap |p is a prime} is not regular

Non deterministic finite state automaton, Automaton (NFA) (with ε-transitio...

Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q 0 , F i where Q, Σ, q 0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}). We must also modify the de?nitions of th

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

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