Non - sl languages, Theory of Computation

Application of the general suffix substitution closure theorem is slightly more complicated than application of the specific k-local versions. In the specific versions, all we had to do was to find two strings in which the same sequence of k - 1 adjacent symbols occurred which when cross-spliced witness the failure of suffix substitution closure. Here we have to be prepared for to show that for any k, such a pair of strings exist. Fortunately, we don't have to show that there is a single pair of strings that works for all k, only that for all k there is some pair. In other words, the pairs we use may depend on k. One useful way to organize this is known as an adversary argument. The theorem can be stated formally as:

579_Non - SL Languages.png

The idea is to interpret this as the rules of a game. You are attempting to show that the property does not hold; your adversary is attempting to show that it does. The universally bound variables (∀L) and (∀u , v , u , v , x) are your choices-your plays. The existentially bound variable (∃k) is your adversary's choice-their plays. The game proceeds from the outside of the formula in:

• You choose L the language you intend to prove is not SL.

• Your adversary, claiming that there is a k-local automaton that recognizes it, chooses k. Presumably, their choice of k will depend on your choice of L. Not even this adversary is going to claim that all languages are SL.

• You now choose two strings u1xv1 and u2xv2. Again, your choice should depend on the specific value of k your adversary chose (as well, of course, as the L you chose to start with).

• You win iff the two strings you chose witness that the language does not satisfy the theorem, i.e., iff

- u1xv1 and u2xv2 are both in L and

- u1xv2 is not in L.

Under this interpretation of the theorem, a proof that a given language is non SL consists of a strategy that always leads to a win whenever you start with L as your initial choice.

Posted Date: 3/22/2013 1:49:38 AM | Location : United States







Related Discussions:- Non - sl languages, Assignment Help, Ask Question on Non - sl languages, Get Answer, Expert's Help, Non - sl languages Discussions

Write discussion on Non - sl languages
Your posts are moderated
Related Questions
i have some questions in automata, can you please help me in solving in these questions?

De?nition (Instantaneous Description) (for both DFAs and NFAs) An instantaneous description of A = (Q,Σ, δ, q 0 , F) , either a DFA or an NFA, is a pair h q ,w i ∈ Q×Σ*, where

proof ogdens lemma .with example i am not able to undestand the meaning of distinguished position .

#Your company has 25 licenses for a computer program, but you discover that it has been copied onto 80 computers. You informed your supervisor, but he/she is not willing to take an

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

Suppose A = (Q,Σ, T, q 0 , F) is a DFA and that Q = {q 0 , q 1 , . . . , q n-1 } includes n states. Thinking of the automaton in terms of its transition graph, a string x is recogn

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

Normal forms are important because they give us a 'standard' way of rewriting and allow us to compare two apparently different grammars G1  and G2. The two grammars can be shown to

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

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