Class of local languages is not closed under union, Theory of Computation

Both L1 and L2 are SL2. (You should verify this by thinking about what the automata look like.)

2360_Class of local languages is not closed under union.png

We claim that L1 ∪ L2 ∈ SL2. To see this, suppose, by way of contradiction, that it was SL2. Then it would satisfy Suffx Substitution Closure. But abb ∈ L1 ∪ L2, since it is in L1, and bba ∈ L1 ∪ L2, since it is in L2, and, by Suffx Substitution Closure, this implies that aba ∈ L1 ∪ L2, which is not the case. Hence, L1 ∪ L2 is not SL2.

It's important to not misunderstand the weight of this result. It does not show that every union of two SL2 languages is not SL2-after all, the union of any SL2 language with itself must, necessarily, be SL2. It is easy to come up with pairs of distinct SL2 languages which yield an SL2 union as well,

1737_Class of local languages is not closed under union1.png

What it does say is that one can't count on the union of SL2 languages being SL2. This is in contrast to the closure result for intersection, which lets us build up languages out of simpler SL2 languages using intersection with con?dence that the result will be SL2. Showing that our desired language is the union of some simple SL2 languages doesn't help us. The result may or may not be SL.

Posted Date: 3/22/2013 12:53:40 AM | Location : United States







Related Discussions:- Class of local languages is not closed under union, Assignment Help, Ask Question on Class of local languages is not closed under union, Get Answer, Expert's Help, Class of local languages is not closed under union Discussions

Write discussion on Class of local languages is not closed under union
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

Prepare the consolidated financial statements for the year ended 30 June 2011. On 1 July 2006, Mark Ltd acquired all the share capitall of john Ltd for $700,000. At the date , J

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

The Equivalence Problem is the question of whether two languages are equal (in the sense of being the same set of strings). An instance is a pair of ?nite speci?cations of regular


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

Computer has a single LIFO stack containing ?xed precision unsigned integers (so each integer is subject to over?ow problems) but which has unbounded depth (so the stack itself nev

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

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 .

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