A context sensitive grammar (CSG) is a grammar where all productions are of the form αAβ → αγβ where γ ≠ ε.

During derivation non-terminal A will be changed to γ only when it is present in the context of α  and β. 

*Note the constraint that the replacement string γ ≠ ε ; as a consequence we have α ⇒ β implies |α| ≤ |β|

CSG is a Noncontracting grammar.

Formal Definition of Context Sensitive Grammar

A context sensitive grammar G = ( N, Σ, P, S), where

• N is a set of non-terminal symbols
• Σ is a set of terminal symbols
• S is the start symbol, and
• P is a set of production rules, of the form αAβ → αγβ , where A in N, α, β ∈ (N ∪ Σ) and γ ∈ (N ∪ Σ)⁺

The production S → ε is also allowed if S is the start symbol and it does not appear on the right side of any production.

Linear Bounded Automata

Linear Bounded Automata (LBA) is a single tape Turing Machine with two special tape symbols call them left marker < and the right marker >.

The transitions should satisfy these conditions:

• It should not replace the marker symbols by any other symbol.
• It should not write on cells beyond the marker symbols.

Thus the initial configuration will be : < q0a1a2a3a4a5…..an >

Real Also Definition of Pushdown Automata

Formal Definition

Formally Linear Bounded Automata is a non-deterministic Turing Machine , M = ( Q, Σ, Γ, δ, ε, q0, <, >, t, r)

• Q is set of all states
• Σ is set of all terminals
• Γ is set of all tape symbols, Σ ⊂ Γ
• δ is set of transitions
• ε is blank symbols or null
• < is left marker and > is right marker
• t is accept state
• r is reject state