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

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

Automata, automata of atm machine

automata of atm machine

Qbasic, Ask question #Minimum 100 words accepte

Ask question #Minimum 100 words accepte

Brain game, If the first three words are the boys down,what are the last th...

If the first three words are the boys down,what are the last three words??

Suffix substitution closure, Our primary concern is to obtain a clear chara...

Our primary concern is to obtain a clear characterization of which languages are recognizable by strictly local automata and which aren't. The view of SL2 automata as generators le

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

Decision Theroy, spam messages h= 98%, m= 90%, l= 80% non spam h=12%, m = 8...

spam messages h= 98%, m= 90%, l= 80% non spam h=12%, m = 8%, l= 5% The organization estimates that 75% of all messages it receives are spam messages. If the cost of not blocking a

Designing finite automata, a finite automata accepting strings over {a,b} e...

a finite automata accepting strings over {a,b} ending in abbbba

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

Transition graphs, We represented SLk automata as Myhill graphs, directed g...

We represented SLk automata as Myhill graphs, directed graphs in which the nodes were labeled with (k-1)-factors of alphabet symbols (along with a node labeled ‘?' and one labeled

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