Simulation
Parameters

Target Language (L)

Pumping Length (p)

String Partition s = xyz

X (prefix) —

Y (loop ×n) —

Z (suffix) —

Pump Count (n)

💡 LIVE INSIGHT

At n=1, the string is in its original form. Try pumping to see if the language rule survives.

Pumping "Y" repeats the loop segment. Watch the a/b balance break — proving this language can't be recognised by any finite state machine.

n = 1

Balanced Pair Language

L₁ = { aⁿbⁿ | n ≥ 0 } — For every 'a' there must be exactly one 'b'.

PUMPED STRING s = x · y¹ · z

a COUNT 4

b COUNT 4

STRING LENGTH 8

RATIO (a:b) 1:1

✓ |xy| = 4 ≤ p = 4

✓ |y| = 2 > 0

X — PREFIX Y — PUMPABLE LOOP Z — SUFFIX

LANGUAGE TEST: ACCEPTED ✓

a Count matches b Count. Sequence accepted.