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arxiv: 2605.04188 · v1 · submitted 2026-05-05 · 💻 cs.SE

A Multi-Agent Consensus Protocol for Stable Software Remodularization

Ahmed F. Ibrahim This is my paper

Pith reviewed 2026-05-08 17:52 UTC · model grok-4.3

classification 💻 cs.SE
keywords software remodularizationmulti-agent consensusasymmetric monotonic concession protocolsoftware architectureevolutionary stabilityPareto optimalityZeuthen strategymodule clustering
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The pith

Software remodularization reduces to a multi-agent negotiation that yields stable Pareto-satisfying decompositions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper reframes automatic software remodularisation as a distributed consensus problem among autonomous agents instead of a single-objective optimization. The agents negotiate module partitions using an Asymmetric Monotonic Concession Protocol that lets each respect its own thresholds on structural cohesion and evolutionary stability. The authors formally prove that the protocol terminates, that concessions stay bounded in line with the Zeuthen Strategy under closed conditions, and that the agreed partitions are locally Pareto optimal. This framing matters because real systems must trade off better internal structure against the risk of breaking stability across versions. Early tests on synthetic data and the Xwork framework show the method matches existing optimizers when stability is loose yet acts to enforce tight stability limits.

Core claim

We reframe software module clustering as a distributed consensus problem among autonomous agents. We introduce an Asymmetric Monotonic Concession Protocol (AMCP) that enables agents to negotiate decompositions that respect multi-attribute utility thresholds. We formally prove the protocol's termination, its bounded concession behaviour consistent with the Zeuthen Strategy under closed-instance conditions, and the local Pareto-satisfactoriness of the resulting partitions. Preliminary experiments on a synthetic benchmark and the Xwork Java framework confirm that our negotiated consensus matches state-of-the-art optimizers when stability budgets are loose, while acting as a circuit breaker to

What carries the argument

The Asymmetric Monotonic Concession Protocol (AMCP), a negotiation rule set in which agents propose module assignments and make monotonic concessions until all parties meet their cohesion and stability utility thresholds.

Load-bearing premise

Agents can accurately specify their multi-attribute utility thresholds for cohesion and stability, and all negotiations occur under closed-instance conditions that let the Zeuthen Strategy bound concessions.

What would settle it

An instance under closed conditions in which the protocol fails to terminate or returns a partition that violates local Pareto-satisfactoriness for at least one agent.

Figures

Figures reproduced from arXiv: 2605.04188 by Ahmed F. Ibrahim.

Figure 1
Figure 1. Figure 1: Concession ratio vs. step for the real Xwork graph. view at source ↗
read the original abstract

Automatic software remodularisation is typically cast as a single-objective optimization problem. While recent metaheuristics have improved search efficiency, real-world architecture recovery must reconcile the conflicting attributes of structural cohesion and evolutionary stability. We reframe software module clustering as a distributed consensus problem among autonomous agents. We introduce an Asymmetric Monotonic Concession Protocol (AMCP) that enables agents to negotiate decompositions that respect multi-attribute utility thresholds. We formally prove the protocol's termination, its bounded concession behaviour consistent with the Zeuthen Strategy under closed-instance conditions, and the local Pareto-satisfactoriness of the resulting partitions. Preliminary experiments on a synthetic benchmark and the Xwork Java framework confirm that our negotiated consensus matches state-of-the-art optimizers when stability budgets are loose, while acting as a "circuit breaker" to enforce strict stability constraints. Extended results on ten further systems, including comparisons with multi-objective evolutionary algorithms and multi-version chains, will be reported in a forthcoming full paper.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper reframes software remodularization as a distributed multi-agent consensus problem and introduces an Asymmetric Monotonic Concession Protocol (AMCP) enabling autonomous agents to negotiate module decompositions that balance structural cohesion and evolutionary stability via multi-attribute utility thresholds. It asserts formal proofs of the protocol's termination, bounded concession behaviour consistent with the Zeuthen Strategy under closed-instance conditions, and local Pareto-satisfactoriness of the resulting partitions. Preliminary experiments on a synthetic benchmark and the Xwork Java framework are described as confirming that the negotiated consensus matches state-of-the-art optimizers under loose stability budgets while acting as a circuit breaker for strict stability constraints; extended results on ten further systems are deferred to a future paper.

Significance. If the formal results can be substantiated, the work would offer a novel distributed alternative to centralized metaheuristics for multi-objective architecture recovery, with potential to enforce stability constraints more reliably in evolving software systems. The explicit linkage to the Zeuthen Strategy and Pareto-satisfactoriness under closed conditions could provide a principled foundation for agent-based negotiation in software engineering, distinguishing it from purely heuristic approaches.

major comments (2)
  1. Abstract: The manuscript asserts formal proofs of termination, bounded concession behaviour consistent with the Zeuthen Strategy under closed-instance conditions, and local Pareto-satisfactoriness, yet supplies no proof sketches, assumptions, lemmas, or counter-examples. These proofs are load-bearing for the central claims and cannot be assessed without them.
  2. Experiments (preliminary results on synthetic benchmark and Xwork): The text provides no explicit check that the reported instances satisfy the closed-instance conditions (fixed utility attributes, modules, and stability budgets with no external updates) required for the Zeuthen bounding argument. Without this verification, the claimed formal guarantees and circuit-breaker behaviour lack support for the evaluated cases.
minor comments (2)
  1. Abstract: The phrase 'multi-attribute utility thresholds for cohesion and stability' is introduced without a forward reference to their formal definition or how agents specify them.
  2. The deferral of extended results (including comparisons with multi-objective evolutionary algorithms) to a future paper leaves the current manuscript's empirical contribution preliminary and limits evaluation of the protocol's broader performance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments, which help clarify how to better substantiate the formal and experimental contributions. We address each major comment below and commit to revisions that directly incorporate the requested details without altering the core claims.

read point-by-point responses

  1. Referee: Abstract: The manuscript asserts formal proofs of termination, bounded concession behaviour consistent with the Zeuthen Strategy under closed-instance conditions, and local Pareto-satisfactoriness, yet supplies no proof sketches, assumptions, lemmas, or counter-examples. These proofs are load-bearing for the central claims and cannot be assessed without them.

    Authors: We agree that the current manuscript does not include the detailed proof sketches, assumptions, lemmas, or counter-examples, making independent assessment difficult despite the abstract's claim of formal proofs. The derivations were omitted for brevity in the initial submission. In the revised version we will add a dedicated section (or appendix) that states the closed-instance assumptions explicitly, provides proof sketches for termination and bounded concessions (aligned with the Zeuthen Strategy), establishes local Pareto-satisfactoriness, and includes boundary counter-examples to delineate where the guarantees hold. This will make the load-bearing formal results fully evaluable. revision: yes

  2. Referee: Experiments (preliminary results on synthetic benchmark and Xwork): The text provides no explicit check that the reported instances satisfy the closed-instance conditions (fixed utility attributes, modules, and stability budgets with no external updates) required for the Zeuthen bounding argument. Without this verification, the claimed formal guarantees and circuit-breaker behaviour lack support for the evaluated cases.

    Authors: We concur that an explicit verification of the closed-instance conditions is required to connect the reported results to the Zeuthen bounding argument and the observed circuit-breaker effect. The preliminary experiments were run under static conditions, but this was not documented. In the revised manuscript we will add a subsection in the experiments section that confirms each instance (synthetic benchmark and Xwork) satisfies fixed utility attributes, fixed modules, and unchanging stability budgets with no external updates during negotiation. This verification will directly support the applicability of the formal guarantees to the evaluated cases. revision: yes

Circularity Check

0 steps flagged

No significant circularity; formal proofs presented as independent arguments under explicit conditions.

full rationale

The paper defines the AMCP protocol and states formal proofs of termination, Zeuthen-consistent bounded concessions (restricted to closed-instance conditions), and local Pareto-satisfactoriness. These are presented as direct mathematical results from the protocol rules rather than reductions to fitted parameters, self-referential definitions, or load-bearing self-citations. The Zeuthen reference functions as an external consistency benchmark, not an imported uniqueness theorem or ansatz. No equations or derivations in the provided text reduce the claimed guarantees to the inputs by construction. Experiments are described at a high level as preliminary confirmation and do not serve as the basis for the formal claims.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the AMCP protocol itself is the primary new artifact introduced.

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Reference graph

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