Linear Bounded Automata

Linear Bounded Automata Visually

Advanced Linear Bounded Automata simulator with step-by-step execution, context-sensitive language recognition, and real-time visualization.

Bounded Tape Context-Sensitive Linear Space Real-time Visualization

What is a Linear Bounded Automata (LBA)?

A Linear Bounded Automaton (LBA) is a restricted type of Turing Machine where the tape head cannot move beyond the boundaries of the input string. The tape is bounded by special endmarker symbols, making it a linear space-bounded computation model.

An LBA is formally defined as M = (Q, Σ, Γ, δ, q₀, F) where the tape is bounded by left endmarker ⊢ and right endmarker ⊣, and the head cannot move beyond these boundaries.

Key Properties:
  • Tape bounded by input length
  • Recognizes context-sensitive languages
  • Linear space complexity
  • More powerful than PDA
  • Less powerful than unrestricted TM
Example Languages:
  • L = {aⁿbⁿcⁿ | n ≥ 1}
  • L = {ww | w ∈ {a,b}*}
  • L = {aⁱbʲcᵏ | i ≤ j ≤ k}
  • Palindromes of even length
  • Context-sensitive grammars

Choose LBA Algorithm

Select from various Linear Bounded Automata implementations

aⁿbⁿcⁿ Language
ww Duplication
Even Palindromes
Ordered abc
Custom LBA
Algorithm Complexity
Time: O(n³) Space: O(n) States: 12

Interactive LBA Simulator

5x
Tape Memory Usage
0 / 0 cells
State: q₀
Tape Bounds: [0, 0]
Step: 0 | Head Position: 0 | Execution Time: 0ms
Quick Test Cases:
Execution Statistics
Total Steps: 0
States Visited: 0
Tape Cells Used: 0
Bounds Violations: 0
Execution Status: Ready
Result: -
Transition Table
State Read Write Move Next
Context-Sensitive Languages
L₁ = {aⁿbⁿcⁿ | n ≥ 1}
Equal counts of a's, b's, and c's
L₂ = {ww | w ∈ {a,b}*}
String followed by its copy
L₃ = {aⁱbʲcᵏ | i ≤ j ≤ k}
Ordered sequence with constraints
Execution Trace
Run the LBA to see step-by-step execution