Advanced Formal Verification of ZKP: Verifying a ZK Instruction

This report describes the formal verification of a zkWasm XOR instruction in zero-knowledge virtual machines, covering how provers translate execution traces into arithmetized tables (memory, bit, range, and execution tables), the challenges of representing dynamic data structures and bitwise ops using only addition and multiplication, and the extensive suite of lemmas and invariants required to ensure a single instruction preserves a valid VM state; it emphasizes the high complexity and the necessity of machine-checked proofs to avoid systemic vulnerabilities in zkVMs.