Computational Properties
Computationally, a context-sensitive language is equivalent with a linear bounded nondeterministic Turing machine, also called a linear bounded automaton. That is a non-deterministic Turing machine with a tape of only kn cells, where n is the size of the input and k is a constant associated with the machine. This means that every formal language that can be decided by such a machine is a context-sensitive language, and every context-sensitive language can be decided by such a machine.
This set of languages is also known as NLIN-SPACE, because they can be accepted using linear space on a non-deterministic Turing machine. The class LIN-SPACE is defined the same, except using a deterministic Turing machine. Clearly LIN-SPACE is a subset of NLIN-SPACE, but it is not known whether LIN-SPACE=NLIN-SPACE. It is widely suspected they are not equal.
Read more about this topic: Context-sensitive Language
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