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

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

Pumping lemma, For every regular language there is a constant n depending o...

For every regular language there is a constant n depending only on L such that, for all strings x ∈ L if |x| ≥ n then there are strings u, v and w such that 1. x = uvw, 2. |u

Graph Connectivity, Let G be a graph with n > 2 vertices with (n2 - 3n + 4)...

Let G be a graph with n > 2 vertices with (n2 - 3n + 4)/2 edges. Prove that G is connected.

Automata answer, build a TM that enumerate even set of even length string o...

build a TM that enumerate even set of even length string over a

Hhhhhhhhhhhhhhhhh, Ask question #hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh...

Ask question #hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhMinimum 100 words accepted#

Defining strictly local automata, One of the first issues to resolve, when ...

One of the first issues to resolve, when exploring any mechanism for defining languages is the question of how to go about constructing instances of the mechanism which define part

Construct a regular expression, Given any NFA A, we will construct a regula...

Given any NFA A, we will construct a regular expression denoting L(A) by means of an expression graph, a generalization of NFA transition graphs in which the edges are labeled with

Context free grammar, A context free grammar G = (N, Σ, P, S)  is in binary...

A context free grammar G = (N, Σ, P, S)  is in binary form if for all productions A we have |α| ≤ 2. In addition we say that G is in Chomsky Normaml Form (CNF) if it is in bi

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