Analysis of Nederlof's algorithm for subset sum

TL;DR

This paper critically examines Nederlof's subset sum proof algorithm, revealing flaws in its consistency and recurrence formula, which undermine its correctness for counting subset sums.

Contribution

The paper identifies and explains specific errors in Nederlof's algorithm, challenging its validity for subset sum counting proofs.

Findings

Nederlof's algorithm's consistency is not maintained.

The recurrence formula used in Nederlof's algorithm is incorrect.

The flaws compromise the algorithm's correctness for subset sum proofs.

Abstract

We show that Nederlof's algorithm [Information Processing Letters, 118 (2017), 15-16] for constructing a proof that the number of subsets summing to a particular integer equals a claimed quantity is flawed because: 1) its consistence is not kept; 2) the proposed recurrence formula is incorrect.