CFL
Simulation

Target Language (L)

Pumping Length (p)

String Partition s = uvxyz

U (prefix) —

V (pump 1 ×n) —

X (center) —

Y (pump 2 ×n) —

Z (suffix) —

Pump Count (n)

💡 LIVE INSIGHT

At n=1, the string is in its original form. Both v and y are pumped simultaneously. Try pumping to break the balance.

In CFL pumping, v and y are pumped simultaneously. They must straddle the parse tree's repeated variable. Watch the language rule break as pumping disrupts the balance.

n = 1

Triple Balance Language

L₁ = { aⁿbⁿcⁿ | n ≥ 1 } — Equal counts of a, b, and c in sequence.

PUMPED STRING s = u · v¹ · x · y¹ · z

a COUNT 3

b COUNT 3

c COUNT 3

LENGTH 9

✓ |vxy| = 2 ≤ p = 3

✓ |vy| = 2 > 0

U — PREFIX V — PUMP₁ X — CENTER Y — PUMP₂ Z — SUFFIX

LANGUAGE TEST: ACCEPTED ✓

All symbol counts satisfy the language rule. Accepted.