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

Create a general algorithm from a checking algorithm, Claim Under the assum...

Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about

CNF, S-->AAA|B A-->aA|B B-->epsilon

S-->AAA|B A-->aA|B B-->epsilon

Define ambiguity in cfg, Define the following concept with an example: a.  ...

Define the following concept with an example: a.    Ambiguity in CFG b.    Push-Down Automata c.    Turing Machine

Strictly local generation automaton, Another way of interpreting a strictly...

Another way of interpreting a strictly local automaton is as a generator: a mechanism for building strings which is restricted to building all and only the automaton as an inexh

Automata, As we are primarily concerned with questions of what is and what ...

As we are primarily concerned with questions of what is and what is not computable relative to some particular model of computation, we will usually base our explorations of langua

Regular languages, LTO was the closure of LT under concatenation and Boolea...

LTO was the closure of LT under concatenation and Boolean operations which turned out to be identical to SF, the closure of the ?nite languages under union, concatenation and compl

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

Gephi, construct a social network from the real-world data, perform some si...

construct a social network from the real-world data, perform some simple network analyses using Gephi, and interpret the results.

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