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

Algorithm for the universal recognition problem, Sketch an algorithm for th...

Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi

Problem solving and programming concepts, The Last Stop Boutique is having ...

The Last Stop Boutique is having a five-day sale. Each day, starting on Monday, the price will drop 10% of the previous day’s price. For example, if the original price of a product

Emptiness problem, The Emptiness Problem is the problem of deciding if a gi...

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. P

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

#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.

Third model of computation, Computer has a single LIFO stack containing ?xe...

Computer has a single LIFO stack containing ?xed precision unsigned integers (so each integer is subject to over?ow problems) but which has unbounded depth (so the stack itself nev

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

First model of computation, Computer has a single unbounded precision count...

Computer has a single unbounded precision counter which you can only increment, decrement and test for zero. (You may assume that it is initially zero or you may include an explici

Numerical integration, what problems are tackled under numerical integratio...

what problems are tackled under numerical integration

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