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

Trees and graphs , Trees and Graphs Overview: The problems for this ...

Trees and Graphs Overview: The problems for this assignment should be written up in a Mircosoft Word document. A scanned hand written file for the diagrams is also fine. Be

Suffix substitution , Exercise Show, using Suffix Substitution Closure, tha...

Exercise Show, using Suffix Substitution Closure, that L 3 . L 3 ∈ SL 2 . Explain how it can be the case that L 3 . L 3 ∈ SL 2 , while L 3 . L 3 ⊆ L + 3 and L + 3 ∈ SL

Dfa to re, c program to convert dfa to re

c program to convert dfa to re

Prepare the consolidated financial statements, Prepare the consolidated fin...

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

Normal forms, how to convert a grammar into GNF

how to convert a grammar into GNF

Defining strictly local automata, One of the first issues to resolve, when ...

One of the first issues to resolve, when exploring any mechanism for defining languages is the question of how to go about constructing instances of the mechanism which define part

Toc, how to understand DFA ?

how to understand DFA ?

Differentiate between dfa and nfa, Differentiate between DFA and NFA. Conve...

Differentiate between DFA and NFA. Convert the following Regular Expression into DFA. (0+1)*(01*+10*)*(0+1)*. Also write a regular grammar for this DFA.

Abstract model for an algorithm solving a problem, These assumptions hold f...

These assumptions hold for addition, for instance. Every instance of addition has a unique solution. Each instance is a pair of numbers and the possible solutions include any third

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