Operations on strictly local languages, Theory of Computation

The class of Strictly Local Languages (in general) is closed under

• intersection but is not closed under

• union

• complement

• concatenation

• Kleene- and positive closure

Proof: For intersection, we can adapt the construction and proof for the SL2 case again to get closure under intersection for SLk. This is still not quite enough for SL in general, since one of the languages may be in SLi and the other in SLj for some i = j. Here we can use the hierarchy theorem to show that, supposing i < j, the SLi language is also in SLj . Then the adapted construction will establish that their intersection is in SL .

For non-closure under union (and consequently under complement) we can use the same counterexample as we did in the SL2 case:

1844_Operations on Strictly Local Languages.png

To see that this is not in SLk for any k we can use the pair

1771_Operations on Strictly Local Languages1.png

which will yield abk-1 a under k-local suffix substitution closure.

2435_Operations on Strictly Local Languages2.png

For non-closure under concatenation we can use the counterexample

The two languages being concatenated are in SL2, hence in SLk for all k ≥ 2 but their concatenation is not in SLk for any k, as we showed in the example above.

Posted Date: 3/22/2013 2:05:18 AM | Location : United States

Related Discussions:- Operations on strictly local languages, Assignment Help, Ask Question on Operations on strictly local languages, Get Answer, Expert's Help, Operations on strictly local languages Discussions

Write discussion on Operations on strictly local languages
Your posts are moderated
Related Questions
And what this money. Invovle who it involves and the fact of,how we got itself identified candidate and not withstanding time date location. That shouts me media And answers who''v

We can then specify any language in the class of languages by specifying a particular automaton in the class of automata. We do that by specifying values for the parameters of the

Ask question #hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhMinimum 100 words accepted#

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

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

how to prove he extended transition function is derived from part 2 and 3

what exactly is this and how is it implemented and how to prove its correctness, completeness...

Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con