Closure properties of recognizable languages, Theory of Computation

Assignment Help:

We got the class LT by taking the class SL and closing it under Boolean operations. We have observed that LT ⊆ Recog, so certainly any Boolean combination of LT languages will also be recognizable. But what about the class of recognizable languages as a whole? Are Boolean combinations of recognizable (not just LT) languages also recognizable. In answering we can use the same methodology we use to show that any language is recognizable: consider what we need to keep track of in scanning a string in order to determine if it belongs to the language or not and then use that information to build our state set.

Suppose, then, that L = L1 ∩ L2, where L1 and L2 are both recognizable. A string w will be in L iff it is in both L1 and L2. Since they are recognizable there exist DFAs A1 and A2 for which L1 = L(A1) and L2 = L(A2). We can tell if the string is in L1 or L2 simply by keeping track of the state of the corresponding automaton. We can tell if it is in both by keeping track of both states simultaneously.


Related Discussions:- Closure properties of recognizable languages

Find a regular expression, Find a regular expression for the regular langua...

Find a regular expression for the regular language L={w | w is decimal notation for an integer that is a multiple of 4}

Computations of sl automata, We will specify a computation of one of these ...

We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea

Myhill-nerode theorem, This close relationship between the SL2 languages an...

This close relationship between the SL2 languages and the recognizable languages lets us use some of what we know about SL 2 to discover properties of the recognizable languages.

Non-determinism - recognizable language, Our DFAs are required to have exac...

Our DFAs are required to have exactly one edge incident from each state for each input symbol so there is a unique next state for every current state and input symbol. Thus, the ne

Path function of a nfa, The path function δ : Q × Σ*→ P(Q) is the extension...

The path function δ : Q × Σ*→ P(Q) is the extension of δ to strings: Again, this just says that to ?nd the set of states reachable by a path labeled w from a state q in an

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...

Transition graph for the automaton, Lemma 1 A string w ∈ Σ* is accepted by ...

Lemma 1 A string w ∈ Σ* is accepted by an LTk automaton iff w is the concatenation of the symbols labeling the edges of a path through the LTk transition graph of A from h?, ∅i to

Programming languages, Different types of applications and numerous program...

Different types of applications and numerous programming languages have been developed to make easy the task of writing programs. The assortment of programming languages shows, dif

Data retriving, i have research method project and i meef to make prposal w...

i have research method project and i meef to make prposal with topic. If this service here please help me

Hhhhhhhhhhhhhhhhh, Ask question #hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh...

Ask question #hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhMinimum 100 words accepted#

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