Closure properties of recognizable languages, Theory of Computation

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.

Posted Date: 3/21/2013 3:06:13 AM | Location : United States







Related Discussions:- Closure properties of recognizable languages, Assignment Help, Ask Question on Closure properties of recognizable languages, Get Answer, Expert's Help, Closure properties of recognizable languages Discussions

Write discussion on Closure properties of recognizable languages
Your posts are moderated
Related Questions
a) Let n be the pumping lemma constant. Then if L is regular, PL implies that s can be decomposed into xyz, |y| > 0, |xy| ≤n, such that xy i z is in L for all i ≥0. Since the le

automata of atm machine

c program to convert dfa to re

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

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

Generate 100 random numbers with the exponential distribution lambda=5.0.What is the probability that the largest of them is less than 1.0?

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

As de?ned the powerset construction builds a DFA with many states that can never be reached from Q′ 0 . Since they cannot be reached from Q′ 0 there is no path from Q′ 0 to a sta

A finite, nonempty ordered set will be called an alphabet if its elements are symbols, or characters. A finite sequence of symbols from a given alphabet will be called a string ove

Let L 3 = {a i bc j | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L 3 . Use the construction of the proof to extend the automaton to one that recognizes L 3 . Gi