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arxiv: 2606.29627 · v1 · pith:AHRSMLNUnew · submitted 2026-06-28 · 📡 eess.SY · cs.SY

A Two-Stage Reflection and Reprompting Framework for LLM-Based Solution of Petri Net Reachability Problems in Industrial Applications

Ruimin Hu , Mehmet Mercang\"oz This is my paper

Pith reviewed 2026-06-30 01:44 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords Petri netsreachability analysislarge language modelsmanufacturing systemsreflection promptingsequence generationdiscrete event systemsscheduling verification
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The pith

A two-stage reflection and reprompting process makes LLMs more accurate at generating feasible sequences for Petri net reachability.

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

The paper aims to show that adding reflection on an initial LLM output followed by a reprompt for clarification reliably increases the success rate of finding valid action sequences that solve reachability queries in Petri net models of manufacturing systems. Direct prompting of LLMs often produces invalid sequences, while conventional solvers face state-space problems; the framework is meant to correct those errors without any model fine-tuning. A reader would care if this holds because manufacturing systems involve concurrent resource use, and faster, more flexible verification could support changing production requirements. Evaluation is limited to six solvable cases on one fixed net structure, with results reported across several LLMs.

Core claim

The combined effects of reflection and re-clarification improve the accuracy of feasible sequence generation. The proposed strategy is assessed on six solvable reachability configurations under a fixed Petri net structure. The results demonstrate improved reliability and stability in solving Petri net reachability problems. The proposed framework is further evaluated across multiple LLMs, which indicates that the framework is not tied to any specific model.

What carries the argument

The two-stage reflection and reprompting mechanism, which first has the LLM reflect on its initial sequence proposal and then issues a clarification prompt to revise it before accepting a final answer.

If this is right

  • More accurate feasible sequences are produced for the tested reachability problems.
  • Reliability and stability increase compared with direct LLM use on the industrial Petri net model.
  • The approach works without fine-tuning and transfers across different LLMs.
  • It provides a way to handle concurrency and resource contention in manufacturing scheduling and verification.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same prompting stages might be tested on reachability problems whose solutions are not known in advance.
  • If the stages reduce invalid outputs, they could be combined with existing graph-search tools to filter candidates.
  • The method suggests that LLMs already encode enough structure about Petri net firing rules for prompting alone to surface it.

Load-bearing premise

Reflection and reprompting will systematically fix LLM mistakes on reachability without creating new invalid sequences or needing any domain-specific training.

What would settle it

Running the framework on the same six reachability configurations and finding that accuracy does not rise or that invalid sequences appear more often than with direct prompting.

Figures

Figures reproduced from arXiv: 2606.29627 by Mehmet Mercang\"oz, Ruimin Hu.

Figure 1
Figure 1. Figure 1: Overall framework of two-stage reflection and reprompting for Petri [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the industrial case study and the associated Petri net [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

Manufacturing systems exhibit strong concurrency, synchronization, and contention for shared reusable resources, which makes fast and reliable scheduling and verification challenging. Petri nets provide a rigorous formalism for modeling such discrete-event manufacturing systems, but reachability analysis and solving remain difficult for conventional graph search or optimization-based solvers, particularly under state-space explosion and evolving production requirements. Recently, Large language models (LLMs) have shown promise as flexible planners that can generate candidate action sequences from textual specifications. However, direct use of LLMs for Petri net reachability remains unreliable. This paper proposes an LLM-based solving framework augmented with a two-stage reflection and reprompting mechanism. The combined effects of reflection and re-clarification improve the accuracy of feasible sequence generation. The proposed method is evaluated on an industrial case modeled as a Petri net. Under a fixed Petri net structure, the proposed strategy is assessed on six solvable reachability configurations. The results demonstrate improved reliability and stability in solving Petri net reachability problems. The proposed framework is further evaluated across multiple LLMs, which indicates that the framework is not tied to any specific model.

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

3 major / 0 minor

Summary. The paper proposes a two-stage reflection and reprompting framework to augment LLMs for solving Petri net reachability problems in manufacturing systems. It claims that the combined reflection and re-clarification stages improve the accuracy of feasible sequence generation, with the strategy evaluated on six solvable reachability configurations under a fixed industrial Petri net structure. The framework is further tested across multiple LLMs to demonstrate generality, and the results are said to show improved reliability and stability compared to direct LLM use.

Significance. If the empirical results hold under proper validation, the approach could offer a flexible, model-agnostic method for handling reachability queries in complex concurrent systems where state-space explosion limits conventional solvers. The explicit multi-LLM evaluation is a strength, as it provides evidence that the framework is not tied to any specific model and supports the claim of improved reliability without domain-specific fine-tuning.

major comments (3)
  1. [Abstract] Abstract and evaluation description: The central claim that reflection and reprompting improve accuracy of feasible sequence generation rests on an evaluation of six solvable cases, yet the manuscript provides no quantitative metrics, error bars, baseline comparisons (e.g., vs. direct prompting or standard reachability algorithms), or details on how success was measured. This is load-bearing because the improvement is presented as an empirical observation without supporting data.
  2. [Evaluation] Evaluation section (implied by abstract): No indication is given of cross-validation of the generated sequences against a standard reachability tool, invariant checker, or explicit firing simulation to confirm that each transition is enabled in sequence and the final marking is reached. Without this, it is impossible to distinguish verified correctness from LLM self-consistency on the fixed net.
  3. [Abstract] The assumption that the two stages systematically correct LLM errors without introducing new invalid sequences is invoked for the six test cases but is not supported by any independent formal check or counter-example analysis, which is required to substantiate the reliability claim.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback highlighting gaps in the evaluation. We will revise the manuscript to strengthen the empirical claims with additional metrics, verification details, and clarifications while preserving the core contribution of the two-stage framework.

read point-by-point responses

  1. Referee: [Abstract] Abstract and evaluation description: The central claim that reflection and reprompting improve accuracy of feasible sequence generation rests on an evaluation of six solvable cases, yet the manuscript provides no quantitative metrics, error bars, baseline comparisons (e.g., vs. direct prompting or standard reachability algorithms), or details on how success was measured. This is load-bearing because the improvement is presented as an empirical observation without supporting data.

    Authors: We agree the current abstract and evaluation lack quantitative support. The revised manuscript will include a table reporting success rates across the six configurations (e.g., fraction of valid sequences), explicit success criteria (sequence enables all transitions in order and reaches target marking), direct-prompting baselines, and variance measures from repeated LLM queries where applicable. revision: yes

  2. Referee: [Evaluation] Evaluation section (implied by abstract): No indication is given of cross-validation of the generated sequences against a standard reachability tool, invariant checker, or explicit firing simulation to confirm that each transition is enabled in sequence and the final marking is reached. Without this, it is impossible to distinguish verified correctness from LLM self-consistency on the fixed net.

    Authors: We accept this point. The revision will add an explicit verification subsection describing use of a Petri-net firing simulator (or equivalent reachability checker) to independently confirm each transition is enabled at its step and the final marking matches the target for all reported sequences. revision: yes

  3. Referee: [Abstract] The assumption that the two stages systematically correct LLM errors without introducing new invalid sequences is invoked for the six test cases but is not supported by any independent formal check or counter-example analysis, which is required to substantiate the reliability claim.

    Authors: The framework's benefit is presented as an empirical observation on the six cases rather than a formal guarantee. The revision will incorporate the independent simulation check noted above and will report any counter-examples or failure modes observed during testing; a general formal proof lies outside the paper's scope given the heuristic character of LLMs. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical evaluation on fixed test cases

full rationale

The paper advances an empirical claim that a two-stage reflection and reprompting framework improves LLM-generated sequence accuracy for Petri net reachability, demonstrated via direct assessment on six solvable configurations of one fixed industrial net and across multiple LLMs. No equations, parameter fittings, or derivations appear in the provided text; the central result is presented as an observed outcome of the evaluation rather than a constructed prediction. No self-citations are invoked as load-bearing premises, and the evaluation does not reduce any reported improvement to its own inputs by definition. The work is therefore self-contained as an empirical study.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper introduces no free parameters, mathematical axioms, or invented entities; the framework is described at the level of prompting stages without additional postulated mechanisms.

pith-pipeline@v0.9.1-grok · 5731 in / 1108 out tokens · 21665 ms · 2026-06-30T01:44:59.637265+00:00 · methodology

discussion (0)

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Reference graph

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