# On modeling hard combinatorial optimization problems as linear programs: Refutations of the "unconditional impossibility" claims

## TL;DR

This paper challenges recent claims that NP-Complete problems cannot be modeled by polynomial-sized linear programs, providing refutations and counterexamples to these assertions.

## Contribution

It offers both general and specific counterexamples to disprove the alleged impossibility of polynomial-sized linear models for NP-Complete problems.

## Key findings

- Counterexamples to the 'unconditional impossibility' claims
- Refutations of recent literature's assertions
- Evidence supporting polynomial-sized linear models for NP-Complete problems

## Abstract

There has been a series of developments in the recent literature (by essentially a same "circle" of authors) with the absolute/unconditioned (implicit or explicit) claim that there exists no abstraction of an NP-Complete combinatorial optimization problem in which the defining combinatorial configurations (such as "tours" in the case of the traveling salesman problem (TSP) for example) can be modeled by a polynomial-sized system of linear constraints. The purpose of this paper is to provide general as well as specific refutations for these recent claims.