Class of local languages is not closed under union, Theory of Computation

Both L1 and L2 are SL2. (You should verify this by thinking about what the automata look like.)

2360_Class of local languages is not closed under union.png

We claim that L1 ∪ L2 ∈ SL2. To see this, suppose, by way of contradiction, that it was SL2. Then it would satisfy Suffx Substitution Closure. But abb ∈ L1 ∪ L2, since it is in L1, and bba ∈ L1 ∪ L2, since it is in L2, and, by Suffx Substitution Closure, this implies that aba ∈ L1 ∪ L2, which is not the case. Hence, L1 ∪ L2 is not SL2.

It's important to not misunderstand the weight of this result. It does not show that every union of two SL2 languages is not SL2-after all, the union of any SL2 language with itself must, necessarily, be SL2. It is easy to come up with pairs of distinct SL2 languages which yield an SL2 union as well,

1737_Class of local languages is not closed under union1.png

What it does say is that one can't count on the union of SL2 languages being SL2. This is in contrast to the closure result for intersection, which lets us build up languages out of simpler SL2 languages using intersection with con?dence that the result will be SL2. Showing that our desired language is the union of some simple SL2 languages doesn't help us. The result may or may not be SL.

Posted Date: 3/22/2013 12:53:40 AM | Location : United States







Related Discussions:- Class of local languages is not closed under union, Assignment Help, Ask Question on Class of local languages is not closed under union, Get Answer, Expert's Help, Class of local languages is not closed under union Discussions

Write discussion on Class of local languages is not closed under union
Your posts are moderated
Related Questions
The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages. Lemma (k-Local Suffix Substitution Clo

Ask question #hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhMinimum 100 words accepted#

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

i want to do projects for theory of computation subject what topics should be best.

Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1's encountered is even or odd.

A Turing machine is a theoretical computing machine made-up by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine having of a line of

Can you say that B is decidable? If you somehow know that A is decidable, what can you say about B?

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

The Equivalence Problem is the question of whether two languages are equal (in the sense of being the same set of strings). An instance is a pair of ?nite speci?cations of regular

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