Universality problem, Theory of Computation

Assignment Help:

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 less work) it can simply be reduced to Emptiness.

Theorem (Universality) The Universality Problem for Regular Languages is decidable.

Proof: L(A) = Σ*⇔ L(A) = ∅. As regular languages are effectively closed under complement we can simply build the DFA for the complement of L(A) and ask if it recognizes the empty language.


Related Discussions:- Universality problem

D c o, Prove xy+yz+ýz=xy+z

Prove xy+yz+ýz=xy+z

Automata, automata of atm machine

automata of atm machine

Fsa as generators, The SL 2 languages are speci?ed with a set of 2-factors...

The SL 2 languages are speci?ed with a set of 2-factors in Σ 2 (plus some factors in {?}Σ and some factors in Σ{?} distinguishing symbols that may occur at the beginning and en

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

Regular expressions, The project 2 involves completing and modifying the C+...

The project 2 involves completing and modifying the C++ program that evaluates statements of an expression language contained in the Expression Interpreter that interprets fully pa

Pendulum Swings, how many pendulum swings will it take to walk across the c...

how many pendulum swings will it take to walk across the classroom?

Prism algorithm, what exactly is this and how is it implemented and how to ...

what exactly is this and how is it implemented and how to prove its correctness, completeness...

Production, How useful is production function in production planning?

How useful is production function in production planning?

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

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