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
In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems

. On July 1, 2010, Harris Co. issued 6,000 bonds at $1,000 each. The bonds paid interest semiannually at 5%. The bonds had a term of 20 years. At the time of issuance, the market r

All that distinguishes the de?nition of the class of Regular languages from that of the class of Star-Free languages is that the former is closed under Kleene closure while the lat

design an automata for strings having exactly four 1''s

let G=(V,T,S,P) where V={a,b,A,B,S}, T={a,b},S the start symbol and P={S->Aba, A->BB, B->ab,AB->b} 1.show the derivation sentence for the string ababba 2. find a sentential form

Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the

I want a proof for any NP complete problem

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

design a tuning machine for penidrome

While the SL 2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless