Concatenation, Theory of Computation

Assignment Help:

We saw earlier that LT is not closed under concatenation. If we think in terms of the LT graphs, recognizing the concatenation of LT languages would seem to require knowing, while scanning a string in L1 . L2, for instance, when to switch from keeping track of factors for L1 to keeping track of factors from L2.

Assuming that the alphabets were not disjoint, there is (evidently, since LT is not closed under concatenation) no way, in general, to know that. For the recognizable languages, on the other hand, we have the convenience of being able to work with non-determinism. We don't actually have to know when to switch from one automaton to the next. Whenever we get to a point in the string that could possibly be the end of the pre?x that is in L1 we can just allow for a non-deterministic choice of whether to continue scanning for A1 (the machine recognizing L1) or to switch to scanning for A2. Since whenever the string is in L1 .  L2 there will be some correct place to switch and since acceptance by a NFA requires only that there some accepting computation, the combined automaton will accept every string in L1 . L2. Moreover, the combined automaton will accept a string iff there is some point at which it can be split into a string accepted by A1 followed by one accepted by A2: it accepts all and only the strings in L1 . L2.


Related Discussions:- Concatenation

Prism algorithm, what exactly is this and how is it implemented and how to ...

what exactly is this and how is it implemented and how to prove its correctness, completeness...

Computer achitecture, what is a bus and draw a single bus structure

what is a bus and draw a single bus structure

Binary form and chomsky normal form, Normal forms are important because the...

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

Flow charts, https://www.google.com/search?q=The+fomula+n%3D%28x%3D0%29%2F%...

https://www.google.com/search?q=The+fomula+n%3D%28x%3D0%29%2F%281%3D2%29.The+value+x%3D0+and+is+used+to+stop+the+algerithin.The+calculation+is+reapeated+using+values+of+x%3D0+is+in

IT PRoject Management, What are the benefits of using work breakdown struct...

What are the benefits of using work breakdown structure, Project Management

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

Distinguish between mealy and moore machine, Distinguish between Mealy and ...

Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1's encountered is even or odd.

Describe the algorithm and draw the transition diagram, 1. Simulate a TM wi...

1. Simulate a TM with infinite tape on both ends using a two-track TM with finite storage 2. Prove the following language is non-Turing recognizable using the diagnolization

First model of computation, Computer has a single unbounded precision count...

Computer has a single unbounded precision counter which you can only increment, decrement and test for zero. (You may assume that it is initially zero or you may include an explici

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