No. If L={1}, where 1 denotes the empty word, then L+=L and hence is finite. As you observed, if L is empty, then L+ is empty. **In all other cases, L+ is infinite**.

## Is Sigma Star an infinite language?

**the alphabet Sigma is finite, and therefore regular**, and the star operation preserves regularity (by the definition of regular languages). Another example of a regular language is the language A of all strings that have the form 00…

## Is Kleene star always regular?

**always yields a regular language**– Computer Science Stack Exchange. Stack Overflow for Teams – Start collaborating and sharing organizational knowledge.

## How do you tell if a language is finite or infinite?

**if the DFA contains n states, and the language contains any string of length n or more, then the language is infinite**. Otherwise, the language is finite. It is limited to strings of length n or less.

## Is a regular language always infinite?

**no, not all regular languages are infinite**.

## What does Σσ ∗ mean?

If Σ is an alphabet then Σ∗ is **the set of strings over Σ**. For example, if Σ is {0,1} then Σ∗ is the set of binary sequences. • The length of a string is the number of symbol occurrences in it.

## Is a * b * a regular language?

**Yes, a*b* represents a regular language**. Language description: Any number of a followed by any numbers of b (by any number I mean zero (including null ^ ) or more times). Some example strings are: {^, a, b, aab, abbb, aabbb, …}

## How do you know if a language is finite?

A finite language is a language containing a finite number of words. The simplest cases are **those containing no words at all, the empty string, and a single string consisting of a single symbol** (e.g. a in your example).

## Is ∅ a language?

The empty string should not be confused with the empty language ∅, which is **a formal language** (i.e. a set of strings) that contains no strings, not even the empty string.

## Is ∅ a regular language?

∅, the empty set, **is a regular expression**.

## How do you know if a language is empty?

The question stems from the fact that you can determine whether a regular language is empty by **using a Turing machine to count the states n in the given FSM**. When you generate all strings from length 0 to n, if the machine accepts any of them then the language is non-empty.

## Is 0 * a regular language?

**Yes, Language {a ^{n} a^{n} | n >= 0} is a regular language**.

## How do you prove that a language is not regular?

**Method to prove that a language L is not regular**

- Select w such that |w| ≥ c.
- Select y such that |y| ≥ 1.
- Select x such that |xy| ≤ c.
- Assign the remaining string to z.
- Select k such that the resulting string is not in L.

## What does Σ ∗ mean?

If Σ is an alphabet then Σ∗ is **the set of strings over Σ**. For example, if Σ is {0,1} then Σ∗ is the set of binary sequences. • The length of a string is the number of symbol occurrences in it.

## Can an alphabet be empty?

An alphabet is a finite, nonempty set. No matter what alphabet we are working with at any time, we call its members symbols. It is reasonable that we must have at least one symbol (so **an alphabet is not allowed to be empty**), and we do not have infinitely many symbols.

## Can a regular language be infinite?

The Wikipedia entry for Regular language states that the all finite languages are regular and that **infinite languages are not regular** because they cannot be recognized by a finite automaton because the finite automaton has access to a finite quantity of memory.

## Is empty set a language?

**The empty set is a language which has no strings**. The set { } is a language which has one string, namely . Though has no symbols, this set has an object in it.

## How do I know my minimum breast pump size?

The minimum pumping length **must always be greater than 0, even if there are no strings in the language**. This should be 2. If p = 1, we can’t pump 01 (because y must equal 0, and 001 is not in the language). This should be 5.

## What does ⊂ mean in math?

A subset is a set whose elements are all members of another set. The symbol “⊆” means “**is a subset of**“. The symbol “⊂” means “is a proper subset of”. Example. Since all of the members of set A are members of set D, A is a subset of D.

## What does an asterisk mean in math?

The asterisk , also called a “star,” is used for a number of different purposed in mathematics. The most common usage is **to denote multiplication** so, for example, . When used as a superscript, the asterisk is commonly voiced ” -star.” A raised asterisk is used to denote the adjoint. , or sometimes the complex conjugate …