Boolean operations - class of recognizable languages, Theory of Computation

Assignment Help:

Theorem The class of recognizable languages is closed under Boolean operations.

The construction of the proof of Lemma 3 gives us a DFA that keeps track of whether or not a given string is in either or both of any pair of recognizable languages. We can modify the construction for other Boolean operations simply by selecting the appropriate set of accepting states:

• Union: Let F′

= {(q, p) | q ∈ F1 or p ∈ F2}. Then L(A′ ) = L1 ∪ L2.

• Relative complement: Let F′ = F1 × (Q2 - F2). Then L(A′ ) = L1 -L2.

• Complement: Let L1 = Σ* and use the construction for relative complement.


Related Discussions:- Boolean operations - class of recognizable languages

How to solve the checking problem, The objective of the remainder of this a...

The objective of the remainder of this assignment is to get you thinking about the problem of recognizing strings given various restrictions to your model of computation. We will w

Hhhhhhhhhhhhhhhhh, Ask question #hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh...

Ask question #hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhMinimum 100 words accepted#

Instantaneous description of an fsa, De?nition Instantaneous Description of...

De?nition Instantaneous Description of an FSA: An instantaneous description (ID) of a FSA A = (Q,Σ, T, q 0 , F) is a pair (q,w) ∈ Q×Σ* , where q the current state and w is the p

Positiveness problem - decision problems, For example, the question of whet...

For example, the question of whether a given regular language is positive (does not include the empty string) is algorithmically decidable. "Positiveness Problem". Note that

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

Strictly 2-local languages, The fundamental idea of strictly local language...

The fundamental idea of strictly local languages is that they are speci?ed solely in terms of the blocks of consecutive symbols that occur in a word. We'll start by considering lan

Strictly 2 - local automata, We will assume that the string has been augmen...

We will assume that the string has been augmented by marking the beginning and the end with the symbols ‘?' and ‘?' respectively and that these symbols do not occur in the input al

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