CODEWITHSUNDEEP
regular-languageturing-machinesdfacomputation-theory
bourne
bourne

Reputation: 1235

Can a Language accept Infinite numbers

I have a question whether a language can accept infinite numbers

I have to reduce Lempty to Linf

where Lempty ={e|L(Pe) is null}
Linf={e|L(Pe) is infinite}

so can i define a program P like this

"
input n
Run Pe on 1...n for n steps
if Pe accept any number then enter an infinite loop and start accepting infinite number
if pe does not accept any number then accept 1"

Now if i can define program P like above then asking the question whether Language accepted by P belong to Linf will tell me whether Language accepted by Pe is null or not.

Any advice or suggestions is always welcome

Upvotes: 0

Views: 244

Answers (1)

The Beruriah Incident
The Beruriah Incident

Reputation: 3257

This question is a bit ill-defined, but here's an approximation: In standard computational theory, languages cannot contain infinite strings. Infinite number is unclear. If you mean a number requiring infinite digits to precisely represent, no. Standard automata cannot recognize infinite length strings (how could it ever terminate?). However, many numbers that appear to require infinite digits (consider one-third as .3333333...) do not require infinite characters to represent otherwise, making them candidates for any language.

Hope that helps, depending on what exactly you're asking.

Upvotes: 1

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