**History :**

In 1960, associate degree automaton model was introduced by **Myhill** and these days this automation model is understood as deterministic linear bounded automaton. After this, another scientist named **Landweber** worked on this and proposed that the languages accepted by a deterministic LBA are continually context-sensitive languages.

In 1964, **Kuroda** introduced a replacement and a lot of general models specially for non-deterministic linear bounded automata, and established that the languages accepted by the non-deterministic linear bounded automata are exactly the context-sensitive languages.

**Introduction to Linear Bounded Automata :**

A Linear Bounded Automaton (LBA) is similar to Turing Machine with some properties stated below:

- Turing Machine with Non-deterministic logic,
- Turing Machine with Multi-track, and
- Turing Machine with a bounded finite length of the tape.

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**Tuples Used in LBA : **

LBA can be defined with eight tuples (elements that help to design automata) as:

M = (Q , T , E , q0 , Mwhere,_{L}, M_{R}, S , F),Q-> A finite set of transition statesT-> Tape alphabetE-> Input alphabetq0-> Initial stateM_{L}_{ }-> Left bound of tapeM-> Right bound of tape_{R}S-> Transition FunctionF-> A finite set of final states

**Diagrammatic Representation of LBA :**

**Examples:**

Languages that form LBA with tape as shown above,

- L = {a
^{n!}| n >= 0} - L = {wn | w from {a, b}+, n >= 1}
- L = {wwwR | w from {a, b}+}

**Facts :**

Suppose that a given LBA M has --> q states, --> m characters within the tape alphabet, and --> the input length is n

- Then M can be in at most f(n) = q * n * mn configurations i.e. a tape of n cells and m symbols, we are able to have solely mn totally different tapes.
- The tape head is typically on any of the n cells which we have a tendency to are typically death penalty in any of the q states.