regular languages

Question

From S1 can we conclude that on any language if we apply some limit then it would be regular?

Comments

yes...if language gets bounded..it becomes regular

Answer 1

Here infinite language means infinite strings of finite length which is true..

But for regularity , the dependency should be restricted so that finite automata can get hold of it..By finite dependency we mean dependencies like strings containing even number of 0's and number of 1's modulo 3 = 1 ..So this can be done by 2 * 3 = 6 states..

Whereas infinite dependency means dependency becomes dependent on a variable ..Let us understand this point more clearly..

Say we have a language L  =  { aⁿ bⁿ | n >= 0 } ..Now for this n can be infinitesimally any large number..So we have to account for all n as we need to ensure b's come after a's and also number of a's  = number of b's and n can be any number..

So this is an infinite dependency as we are depending on the value of n which we dont know..So this is beyond the scope of finite automata..

Hence both the statements S1 and S2 are true..