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?

Well, 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?

Kleene star of an infinite unary language 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?

The key idea is that 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?

The definition of regular language includes the empty set. It also includes the singleton language {a} , so 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, …}

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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 {an an | 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
  1. Select w such that |w| ≥ c.
  2. Select y such that |y| ≥ 1.
  3. Select x such that |xy| ≤ c.
  4. Assign the remaining string to z.
  5. 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.

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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 …

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