- Automata Theory Tutorial
- Automata Theory - Home
- Automata Theory Introduction
- Deterministic Finite Automaton
- Non-deterministic Finite Automaton
- NDFA to DFA Conversion
- DFA Minimization
- Moore & Mealy Machines
- Classification of Grammars
- Introduction to Grammars
- Language Generated by Grammars
- Chomsky Grammar Classification
- Regular Grammar
- Regular Expressions
- Regular Sets
- Arden's Theorem
- Constructing FA from RE
- Pumping Lemma for Regular Grammar
- DFA Complement
- Context-Free Grammars
- Context-Free Grammar Introduction
- Ambiguity in Grammar
- CFL Closure Properties
- CFG Simplification
- Chomsky Normal Form
- Greibach Normal Form
- Pumping Lemma for CFG
- Pushdown Automata
- Pushdown Automata Introduction
- Pushdown Automata Acceptance
- PDA & Context Free Grammar
- PDA & Parsing
- Turing Machine
- Turing Machine Introduction
- Accepted & Decided Language
- Multi-tape Turing Machine
- Multi-Track Turing Machine
- Non-Deterministic Turing Machine
- Semi-Infinite Tape Turing Machine
- Linear Bounded Automata
- Decidability
- Language Decidability
- Undecidable Language
- Turing Machine Halting Problem
- Rice Theorem
- Post Correspondence Problem
- Automata Theory Useful Resources
- Automata Theory - Quick Guide
- Automata Theory - Useful Resources
- Automata Theory - Discussion
Linear Bounded Automata
A linear bounded automaton is a multi-track non-deterministic Turing machine with a tape of some bounded finite length.
Length = function (Length of the initial input string, constant c)
Here,
Memory information ≤ c × Input information
The computation is restricted to the constant bounded area. The input alphabet contains two special symbols which serve as left end markers and right end markers which mean the transitions neither move to the left of the left end marker nor to the right of the right end marker of the tape.
A linear bounded automaton can be defined as an 8-tuple (Q, X, ∑, q0, ML, MR, δ, F) where −
Q is a finite set of states
X is the tape alphabet
∑ is the input alphabet
q0 is the initial state
ML is the left end marker
MR is the right end marker where MR ≠ ML
δ is a transition function which maps each pair (state, tape symbol) to (state, tape symbol, Constant ‘c’) where c can be 0 or +1 or -1
F is the set of final states
A deterministic linear bounded automaton is always context-sensitive and the linear bounded automaton with empty language is undecidable..