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Subjects>Engineering & Technology>Computer Science

How does every language reduce to its complement?

Hilbert Boehm ∙

Lvl 10

∙ 2mo ago

Updated: 2/7/2025

Every language can be reduced to its complement by taking the set of all possible strings and removing the strings that are in the original language. This process results in the complement language, which consists of all strings not in the original language.

AnswerBot

∙ 2mo ago

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Continue Learning about Computer Science

How can you prove that the complement of a regular language is regular?

The complement of a regular language is regular because regular languages are closed under complementation. This means that if a language is regular, its complement is also regular.

Is the context-free language closed under complement?

No, the context-free language is not closed under complement.

What is the complement of a regular language and how does it relate to the concept of regular expressions?

The complement of a regular language is the set of all strings that are not in the original language. In terms of regular expressions, the complement of a regular language can be represented by negating the regular expression that defines the original language.

Is every finite language regular?

No, not every finite language is regular.

What is the complement of a DFA and how does it relate to the original DFA?

The complement of a Deterministic Finite Automaton (DFA) is another DFA that accepts the opposite language of the original DFA. This means that the complement DFA accepts all strings that the original DFA does not accept, and vice versa. The complement DFA is created by swapping the accepting and non-accepting states of the original DFA.

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