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)

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

Parse Tree Resonance Field

L₁: Equal counts of a, b, and c in sequence. String: aⁿbⁿcⁿ

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

PARSE TREE: STABLE

All symbol counts satisfy the language rule. Accepted.