Operations on strictly local languages, Theory of Computation

Assignment Help:

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.


Related Discussions:- Operations on strictly local languages

Gastric juice, what are composition and its function of gastric juice

what are composition and its function of gastric juice

Answer, And what this money. Invovle who it involves and the fact of,how we...

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

Transition and path functions, When an FSA is deterministic the set of trip...

When an FSA is deterministic the set of triples encoding its edges represents a relation that is functional in its ?rst and third components: for every q and σ there is exactly one

Algorithm for the universal recognition problem, Sketch an algorithm for th...

Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi

Turing machine, Design a turing machine to compute x + y (x,y > 0) with x a...

Design a turing machine to compute x + y (x,y > 0) with x an y in unary, seperated by a # (descrition and genereal idea is needed ... no need for all TM moves)

Flow charts, https://www.google.com/search?q=The+fomula+n%3D%28x%3D0%29%2F%...

https://www.google.com/search?q=The+fomula+n%3D%28x%3D0%29%2F%281%3D2%29.The+value+x%3D0+and+is+used+to+stop+the+algerithin.The+calculation+is+reapeated+using+values+of+x%3D0+is+in

Turing machine , Let ? ={0,1} design a Turing machine that accepts L={0^m ...

Let ? ={0,1} design a Turing machine that accepts L={0^m 1^m 2^m } show using Id that a string from the language is accepted & if not rejected .

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