# What Does It Mean If A Language Is Closed?

## What does it mean when a language is closed?

what is a closure Remember that a set S is closed under an operation X if the output of X is in S every time the inputs were in S. So, for example, if you say that regular languages ​​are closed under union, that means that if P and R are regular languages, so is the union of P and R.

## Under what ordinary languages ​​are they closed?

Ordinary languages ​​end in union, concatenation, asterisk, and padding.

## Can an ordinary language be infinite?

(Klynes Theorem) A language is regular if and only if it can be obtained from finite languages ​​by the three operations union, concatenation, repetition a finite number of times. … And it is an infinite language. Therefore, by Kleene’s theorem, it cannot be a regular language.

## How to know if the language is correct?

Every finite set is a regular language. Example 1. All strings of length = 2 in {a, b} *, ie L = {aa, ab, ba, bb} are correct. Given an irregular linguistic expression, but the parameter value is bounded by a constant, the language is regular (that is, it has some kind of finite comparison).

## Are ordinary languages ​​closed in a certain distinction?

3.1 Conclusion on operations on sets. … It is clear that the set of all languages ​​is closed in all general operations on sets. The union/intersection/complement/difference of a rowset always results in a rowset.

## Is the family of regular languages ​​closed by infinite intersections?

Each of them is normal because it only contains one row. But the infinite union is the set {0 i 1 i | i> = 0}, which, as we know, is not regular. Therefore, the infinite union cannot be closed for regular languages.

## Are ordinary sets closed by concatenation?

The set of regular languages ​​is closed by concatenation, union, and Kleene closure. … If a regular expression is the regular language it denotes, then it is denoted by a regular expression, and thus also by a regular.

## What language do state machines accept?

Alternatively, a normal language can be defined as a language recognized by a state machine. The equivalence between regular expressions and finite automata is known as Kleene’s theorem (after American mathematician Stephen Cole Kleene).

## How to demonstrate an infinite language?

If an infinite language is regular, it can be defined by dfa. dfa has a finite number of states (for example, n). Since the language is infinite, some strings in the language must have length > n. For a character string of length > n accepted by dfa, the execution of dfa must contain a loop.

## Is A*b* a common language?

Yes, a * b * represents normal language. Language description: any number from a to followed by any number from b (by any number I mean zero (including zero ^) or more). Here are some example strings: {^, a, b, aab, abbb, aabbb, …}

## Kfg normal?

All regular grammars are contextless, but not all contextless grammars are regular. However, the following context-free grammar is also regular. This grammar is regular: no rule has more than one nonterminal in its right element, and each of these nonterminals is at the same endpoint as the right element.

## Is it a regular language closed by infinite union?

Each of them is normal because it only contains one row. But the infinite union is the set {0 i 1 i | i> = 0}, which, as we know, is not regular. Therefore, the infinite union cannot be closed for regular languages.