Why Turing machine called linear bounded automata?

An LBA differs from a Turing machine in that while the tape is initially considered to have unbounded length, only a finite contiguous portion of the tape, whose length is a linear function of the length of the initial input, can be accessed by the read/write head; hence the name linear bounded automaton.

Which grammar is accepted by linear bounded automata?

LEM~A 4. For any linear-bounded grammar G there exists a linear- bounded automaton which accepts the language L(G) generated by G. It follows immediately from these lemmas that for any context-sensi- tive language there exists a linear-bounded automaton which generates it.

How many tuples are there in linear bounded automata?

10 A nondeterministic linear bounded automaton (LBA) µ is a 5-tuple (A, Q, δ, q0,F) where the components are defined as fol- lows: A – The tape alphabet, defined as Σ ∪ {>, <, ⊔}. These extra symbols are the left and right end markers and empty symbol respectively.

What is the context sensitive grammar and linear bounded automata LBA?

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. CSG is a Noncontracting grammar.

Is Linear Bounded Automata more powerful than Turing machine?

If the length limit were a constant, then the machine would be no more powerful than a DFA. However, a DFA cannot grow more states to cope with a longer input, which in effect the LBTM can do (taking the state to be the entire machine configuration.) So the LBTM is strictly more powerful.

What is LBA in automata theory?

Definition. A Turing machine that uses only the tape space occupied by the input is called a linear-bounded automaton (LBA). A linear bounded automaton is a nondeterministic Turing machine M = (Q,Σ,Γ, δ,s,t,r) such that: There are two special tape symbols < and >(the left end marker and right end marker).