What is context sensitive grammar with example?

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. Thus, CSG are positioned between context-free and unrestricted grammars in the Chomsky hierarchy.

How do you know if a grammar is context-sensitive?

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. An equivalent construct would be a pushdown automaton. It’s the same as DFA, but with a stack available.

Which mathematical model is for context-sensitive language?

Context-free languages are described by context-free grammars, which can be generated by pushdown automata. Regular languages and finite state machines can describe some context-free languages, but not all. Turing machines can generate all regular languages, all context-free languages, and more.

Is L1 ∩ L2 is a context free language?

Intersection − If L1 and L2 are context free languages, then L1 ∩ L2 is not necessarily context free. Intersection with Regular Language − If L1 is a regular language and L2 is a context free language, then L1 ∩ L2 is a context free language.

Is CSL closed under complement?

Context sensitive languages are closed under union, intersection, complement, concatenation, kleene star, reversal. Every Context sensitive language is recursive. Proof for other closure properties There is a recursive language that is not context-sensitive.

What is the complement of CSL?

Context-sensitive Language: The language that can be defined by context-sensitive grammar is called CSL. Properties of CSL are : Union, intersection and concatenation of two context-sensitive languages is context-sensitive. Complement of a context-sensitive language is context-sensitive.

Which one of the following production rules is correct for a context-sensitive grammar?

Production Rule: aAb->agb belongs to which of the following category? Explanation: Context Sensitive Language or Type 1 or Linearly Bounded Non deterministic Language has the production rule where the production is context dependent i.e. aAb->agb.

Is complement of CSL is CSL?

What is closure property in automata?

Closure properties on regular languages are defined as certain operations on regular language which are guaranteed to produce regular language. Closure refers to some operation on a language, resulting in a new language that is of same “type” as originally operated on i.e., regular.

Is a complement of a CFL always a CFL?

Neither statement is true. 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.

Is every CSL is recursive?

So G is a context sensitive grammar, L(G) is a CSL. Every context-sensitive language L is recursive.

How do you remember Closure property?

In short, closure property is applicable, only when a language is closed under an operation. Now, while applying closure property do remember the language hierarchy. Regular ⊂ DCFL ⊂CFL ⊂ REC ⊂ RE. So, if CFL is closed under Union, and L1 and L2 belong to CFL, then L1∪L2 will be a CFL.