What is the complement of a context free language?

Asked By: Phyllis Batchyanskas | Last Updated: 27th March, 2020
Category: technology and computing programming languages
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The complement of a context-free language can be context-free or not; the complement of a non-context free language can be context-free or not. Every regular language is context-free. Regular languages are closed under complement, so the complement of a regular language is regular.

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Similarly, what is the complement of a language?

In grammar, a complement is a word, phrase, or clause that is necessary to complete the meaning of a given expression. Complements are often also arguments (expressions that help complete the meaning of a predicate). There are indicative as well as non-indicative complements in languages.

Furthermore, what is context free language with example? In formal language theory, a context-free language (CFL) is a language generated by a context-free grammar (CFG). Context-free languages have many applications in programming languages, in particular, most arithmetic expressions are generated by context-free grammars.

Also Know, what do you mean by context free language?

Context-free Languages. In formal language theory, a language is defined as a set of strings of symbols that may be constrained by specific rules. A valid (accepted) sentence in the language must follow particular rules, the grammar. A context-free language is a language generated by a context-free grammar.

What is complement of CFL?

One can understand your question in two ways, according to the definition of "the complement of CFL". case A: Complement of CFL is the class of all the languages that are not in CFL. Formally, ¯CFL={L∣L∉CFL}. In that case, ¯CFL is way bigger than P, it even has languages that are not in R, etc.

37 Related Question Answers Found

What is the complement of the language accepted by the NFA?

What is the complement of the language accepted by the NFA shown below? Explanation: The given alphabet contains only one symbol {a} and the given NFA accepts all strings with any number of occurrences of 'a'. In other words, the NFA accepts a+. Therefore complement of the language accepted by automata is empty string.

Is regular language closed under intersection?

Regular Languages are closed under intersection, i.e., if L1 and L2 are regular then L1 ∩ L2 is also regular.

How do you find the complement of a regular expression?

1 Answer
  1. Construct the corresponding NFA.
  2. Create its equivalent DFA.
  3. Take DFA's complement (change accepting states to non-accepting and vice versa)
  4. Derive the corresponding regex from the DFA of the previous step.

Are non regular languages closed under complement?

Non regular languages are closed under reverse, because L=(LR)R. Same is true for complement. Non regular languages are not closed under most other basic operations though. There is no complete list of operations on languages, so a complete answer cannot be given.

How do you convert NFA to DFA?


Steps for converting NFA to DFA:
  1. Step 1: Initially Q' = ϕ
  2. Step 2: Add q0 of NFA to Q'.
  3. Step 3: In Q', find the possible set of states for each input symbol.
  4. Step 4: In DFA, the final state will be all the states which contain F(final states of NFA)

What is Kleene's theorem in automata?

Contents. In this unit we are going to learn Kleene's theorem. It states that any regular language is accepted by an FA and conversely that any language accepted by an FA is regular. Theorem 1 (Part 1 of Kleene's theorem): Any regular language is accepted by a finite automaton.

Is English context free?

Quite simply, a context free language is a language that can be generated by a context free grammar. Some languages are context free, and some are not. For example, it seems plausible that English is a context free language.

What is context in grammar?

A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are less general (in the same sense) than unrestricted grammars.

Where can I find context free language?

3 Answers. First, you should attempt to build a context-free grammar that forms the language in subject. A grammar is context-free if left-hand sides of all productions contain exactly one non-terminal symbol. By definition, if one exists, then the language is context-free.

What are the applications of context free grammar?


1 Answer. Context-free grammars are used in compilers and in particular for parsing, taking a string-based program and figuring out what it means. Typically, CFGs are used to define the high-level structure of a programming language.

What does CFG mean?

chubby fat girl

What is the difference between regular language and context free language?

Regular grammar is either right or left linear, whereas context free grammar is basically any combination of terminals and non-terminals. Since regular grammars are non-ambiguous, there is only one production rule for a given non-terminal, whereas there can be more than one in the case of a context-free grammar.

Is any finite language context free?

Every finite language is context-free, and therefore A ∩ B context-free. Finally, given that we have proved that both A ∩ B and A ∩ B are context-free, it holds that A Δ B = (A ∩ B) ∪ (A ∩ B) is context-free because the union of two context-free languages is necessarily context-free.

What are the closure properties of context free languages?

Closure Properties of Context Free Languages. L3 = L1 ∪ L2 = { anbncm ∪ anbmcm | n >= 0, m >= 0 } is also context free. L1 says number of a's should be equal to number of b's and L2 says number of b's should be equal to number of c's. Their union says either of two conditions to be true.

How do I convert to normal form in Greibach?


Algorithm to Convert a CFG into Greibach Normal Form
  1. Step 1 − If the start symbol S occurs on some right side, create a new start symbol S' and a new production S' → S.
  2. Step 2 − Remove Null productions. (
  3. Step 3 − Remove unit productions. (
  4. Step 4 − Remove all direct and indirect left-recursion.

How do you prove a language is regular?

To prove a language is regular: construct a DFA, NFA or RE that recognizes it. To prove a language is not regular: show that recognizing it requires keeping track of infinite state (hard to be completely convincing in most cases) or use the pumping lemma to get a contradiction.

What is the difference between context free and context sensitive grammar?

Originally Answered: What is the difference between context free grammar and context sensitive grammar? If a grammar has any productions that have something other than just one nonterminal on the LHS, it's context-sensitive; otherwise, it's context free.