Linear bounded automaton

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A linear bounded automaton (plural linear bounded automata, abbreviated LBA) is a restricted form of a non-deterministic Turing machine. It possesses a tape made up of cells that can contain symbols from a finite alphabet, a head that can read from or write to one cell on the tape at a time and can be moved, and a finite number of states. It differs from a Turing machine in that while the tape is initially considered infinite, only a finite contiguous portion whose length is a linear function of the length of the initial input can be accessed by the read/write head. This limitation makes an LBA a more accurate model of computers that actually exist than a Turing machine in some respects.

Linear bounded automata are accepters for the class of context-sensitive languages. The only restriction placed on grammars for such languages is that no production maps a string to a shorter string. Thus no derivation of a string in a context-sensitive language can contain a sentential form longer than the string itself. Since there is a one-to-one correspondence between linear-bounded automata and such grammars, no more tape than that occupied by the original string is necessary for the string to be recognized by the automaton.

Automata theory: formal languages and formal grammars
Chomsky hierarchy	Grammars	Languages	Minimal automaton
Type-0	Unrestricted	Recursively enumerable	Turing machine
n/a	(no common name)	Recursive	Decider
Type-1	Context-sensitive	Context-sensitive	Linear-bounded
n/a	Indexed	Indexed	Nested stack
Type-2	Context-free	Context-free	Nondeterministic Pushdown
n/a	Deterministic Context-free	Deterministic Context-free	Deterministic Pushdown
Type-3	Regular	Regular	Finite
Each category of languages or grammars is a proper subset of the category directly above it.