If language L 1 is regular and language L 2 is regular, which of the following i

Question

If language L1 is regular and language L2 is regular, which of the following is/are also regular?

a. L1 ? L2

b. L1 ? L2

c. L1L2

d. L1*

e. all of the above

The language of strings that start with a and have 4 b's and have length < 8 is regular.

Select one:

a. true

b. false

I know this one is true since I already got it wrong, but why is it true? I thought Finite State Machines cannot store or count strings and any problem that requires it is not a regular language. How would you draw a DFA that gives the choice between a or b after the first a and still verify there's 4 b's somewhere mixed in there without enforcing them at specific locations?

Explanation / Answer

Theory of Computation | Union & Intersection of Regular languages with CFL

Essential – Chomsky Hierarchy, Regular Languages

As we as a whole know that dialects acknowledged by limited automata are called standard dialects and those which are acknowledged by push down automata are called setting free dialects But, with regards to the association or crossing point of these two dialects a few people think that its hard to dissect whether the convergence brings about a consistent or a setting free dialect.

The main thing to watch is each general dialect is really setting free,the reason is very straightforward. One approach to call a dialect standard is by planning its comparable limited automata or at the end of the day in the event that we can outline a limited automata for a specific dialect then no one but we can call that dialect – customary and same exists for setting free dialects, on the off chance that it is conceivable to plan a push down automata for a specific dialect then just it is called setting free.

Presently a push down automata in basic words is really a limited automata with a memory gave to it as vast stack. What you have to watch that is conceivable to plan a limited automata for a specific dialect then it is additionally conceivable to outline its proportionate push down automata what we need to do is simply not to utilize the endless stack accessible in it. Its that basic. Watch this lastly what will you get is that for each general dialect it is conceivable to outline limited automata and along these lines push down automata. This is the motivation behind why each customary dialect can likewise be called setting free or at the end of the day consistent dialects are subset of setting free dialects.

Association of Regular dialect with setting free dialect –

As every customary dialect are sans setting the association of the two outcomes in a setting free dialect. Be that as it may, it is constantly great to comprehend with the assistance of an illustration.

We should take a dialect L1 = {0*1*} (standard) and L2 = {0^n1^n |n>=0} (setting free)

Also, let L=L1 U L2 which will bring about association of both these dialects and that will be :

L = {0*1*} which is customary dialect yet since each standard dialect is without setting. In this way, we can state the association of two dependably brings about setting free dialect.

Crossing point of Regular dialect with setting free dialect –

Since now we realize that every standard dialect are subset of setting free there is no issue in understanding the association of two however when we discuss crossing point again the appropriate response is sans setting dialect. Truly, the convergence of a standard and a setting free dialect dependably result in a setting free dialect.

We should again take the above case in which L1 and L2 are same yet now let

L= L1 ? L2 which will effortlessly bring about

L={0^n1^n | n>=0} which is without setting .

You can take all the more such cases and check that the association and crossing point of a normal dialect and a setting free dialect dependably brings about a setting free dialect.

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