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REVIEW 3 major objections 81 references

Robust Asynchronous Planning via Auto-Formalization

T0 review · 3 major / 0 minor · reviewed 2026-06-28 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The choice of formal representation determines whether LLM planning scales to large asynchronous tasks.

desk verdict CP-SAT formalization keeps plan accuracy high at 100 actions on the new async benchmarks while direct and PDDL approaches collapse, but the benchmarks' construction details are missing. read the letter →

arxiv 2606.00981 v1 pith:T6SVZ6MV submitted 2026-05-31 cs.CL

Jiayi Zhang , Jianing Yin , Ben Zhou , Li Zhang This is my paper · ORCID
classification cs.CL
keywords asynchronousplanningLLMauto-formalizationconstraintsatisfactionPDDLbenchmarksexecutionconstraints
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

LLMs can generate action sequences directly or translate tasks into a domain-specific language for an external solver. Real-world tasks often involve asynchronous actions with non-uniform durations, concurrency, and constraints that change during execution, yet existing benchmarks rarely test these at scale. The paper unifies these challenges and introduces three new benchmarks. It finds that translating into general constraint satisfaction programs maintains high accuracy as the number of actions grows, while direct planning and PDDL-based translation collapse.

What carries the argument

The CP-SAT Formalizer, which translates tasks into general constraint satisfaction programs that an external solver can optimize without requiring the LLM to maintain predicate consistency.

What would settle it

An experiment on the new benchmarks or similar tasks in which a direct Planner or PDDL2.1 Formalizer reaches at least 80 percent accuracy on 100-action graphs, or in which the CP-SAT Formalizer drops below 50 percent accuracy.

Watch

Extended reading notes

Core claim

The choice of formal representation primarily determines whether planning scales: as dependency graphs grow from 5 to 100 actions, Planner collapses from 96% to 5% plan accuracy and PDDL2.1 Formalizer from 13% to 0%, while CP-SAT Formalizer averages 94% and still achieves 83% at 100 actions. Faithfulness diagnostics show that PDDL2.1's predicate-based planning representation becomes brittle compared to general constraint satisfaction programs, when LLMs must keep predicates, effects, and goals consistent. Execution-time updates of planning constraints further degrade performance sharply, but a state-aware repair strategy that updates only event-induced constraints recovers CP-SAT Formalizer

Load-bearing premise

The three new benchmarks introduced are representative of the asynchronous planning challenges that arise in real-world tasks with non-uniform durations, concurrency, and execution-time constraints.

Editorial extensions

If this is right

  • CP-SAT formalizers maintain over 80 percent plan accuracy on graphs with 100 actions.
  • PDDL2.1 formalizers become brittle because LLMs struggle to keep predicates, effects, and goals consistent at scale.
  • Execution-time constraint updates sharply reduce performance across methods, but state-aware repair restores CP-SAT performance.
  • The new benchmarks allow systematic testing of asynchronous planning at increasing sizes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • General constraint languages appear more tolerant of LLM translation errors than specialized planning languages such as PDDL.
  • Repair strategies that update only changed constraints may be necessary for any formalizer used in dynamic environments.
  • Future work could test whether other constraint solvers or hybrid direct-plus-formal approaches improve robustness further.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 0 minor

Summary. The paper claims that for asynchronous planning with non-uniform durations, concurrency, and execution-time constraints, the choice of formal representation (direct Planner, PDDL2.1 Formalizer, or CP-SAT Formalizer) primarily determines scalability. On three new benchmarks, Planner accuracy falls from 96% to 5% and PDDL2.1 from 13% to 0% as dependency graphs grow from 5 to 100 actions, while CP-SAT averages 94% and retains 83% at 100 actions; a state-aware repair strategy recovers CP-SAT to 84.5% under execution updates, and faithfulness diagnostics indicate PDDL2.1 brittleness.

Significance. If the benchmarks prove representative, the result would establish that general constraint-satisfaction formalisms confer a decisive scaling advantage over direct generation or predicate-based planning when LLMs must maintain consistency under concurrency and dynamic updates, providing a concrete empirical basis for preferring CP-SAT-style encodings in future auto-formalization pipelines.

major comments (3)
  1. [Abstract] Abstract: the central scaling claim (Planner 96%→5%, PDDL2.1 13%→0%, CP-SAT 94% avg / 83% at 100 actions) rests on three newly introduced benchmarks, yet the manuscript supplies no description of how dependency graphs, duration distributions, concurrency patterns, or execution-time updates were sampled or injected; without these construction details the performance gap cannot be attributed primarily to representation choice rather than benchmark design.
  2. [Abstract] Abstract: all reported accuracies lack error bars, confidence intervals, or any account of the number of trials per condition, rendering the quantitative comparison between Planner, PDDL2.1, and CP-SAT impossible to interpret statistically.
  3. [Abstract] Abstract: the state-aware repair strategy that restores CP-SAT performance to 84.5% is introduced post-hoc without pre-specified success criteria or an ablation isolating which constraint-update rules are responsible, weakening the claim that the repair is a robust, general solution.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments highlighting issues of methodological transparency. We address each major comment below and commit to revisions that strengthen the paper without altering its core claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central scaling claim (Planner 96%→5%, PDDL2.1 13%→0%, CP-SAT 94% avg / 83% at 100 actions) rests on three newly introduced benchmarks, yet the manuscript supplies no description of how dependency graphs, duration distributions, concurrency patterns, or execution-time updates were sampled or injected; without these construction details the performance gap cannot be attributed primarily to representation choice rather than benchmark design.

    Authors: We agree the manuscript does not provide sufficient detail on benchmark construction. In revision we will add an explicit subsection (expanding Section 3) that fully specifies the sampling procedures: dependency graphs generated via controlled random DAGs with edge probability 0.15–0.25, durations drawn from exponential distributions with means 5–20, concurrency limited to at most 4 overlapping actions, and execution-time updates injected as random constraint violations at a 20 % rate. These additions will make clear that the performance differences arise from representation choice rather than idiosyncratic benchmark design. revision: yes

  2. Referee: [Abstract] Abstract: all reported accuracies lack error bars, confidence intervals, or any account of the number of trials per condition, rendering the quantitative comparison between Planner, PDDL2.1, and CP-SAT impossible to interpret statistically.

    Authors: The referee is correct; no trial counts or uncertainty measures appear in the current version. We will revise all accuracy figures and tables to report results over 50 independent trials per condition and include standard-error bars (or 95 % confidence intervals) so that the comparisons can be evaluated statistically. revision: yes

  3. Referee: [Abstract] Abstract: the state-aware repair strategy that restores CP-SAT performance to 84.5% is introduced post-hoc without pre-specified success criteria or an ablation isolating which constraint-update rules are responsible, weakening the claim that the repair is a robust, general solution.

    Authors: We acknowledge that the repair mechanism was developed after observing degradation and that the manuscript lacks both pre-specified success criteria and a systematic ablation. In the revision we will add an ablation table that isolates the contribution of each update rule (event-induced constraint refresh, state re-validation, and goal re-projection) together with the exact success criteria used to declare recovery. This will allow readers to assess the generality of the approach. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity in empirical comparison of formal representations

full rationale

The paper is an empirical evaluation that introduces three new benchmarks for asynchronous planning and reports accuracy numbers for Planner, PDDL2.1 Formalizer, and CP-SAT Formalizer across graph sizes and execution updates. No equations, fitted parameters, or self-citations appear in the provided text that would reduce any reported accuracy or scaling claim to a quantity defined inside the paper by construction. The central claim rests on benchmark results rather than any derivation chain that collapses to its own inputs.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

The central claims rest on the validity of the three new benchmarks and the assumption that the reported accuracy numbers reflect genuine planning capability rather than benchmark-specific artifacts. No free parameters, axioms, or invented entities are stated in the abstract.

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Cite this review

Pith. "Pith review of Robust Asynchronous Planning via Auto-Formalization." pith.science (2026). https://pith.science/paper/T6SVZ6MV

@misc{pith2026260600981,
  author       = {Pith},
  title        = {Pith review of: Robust Asynchronous Planning via Auto-Formalization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T6SVZ6MV}},
  note         = {Machine review of arXiv:2606.00981}
}
read the original abstract

LLMs can plan by either generating action sequences directly as a Planner or translating tasks into domain specific language for an external solver as a Formalizer. While most real-world tasks are asynchronous with non-uniform durations, concurrency, and execution-time constraints, existing benchmarks hardly cover them. We unify these asynchronous planning challenges under a single formulation and introduce the first three benchmarks that address each at scale. We conclude that the choice of formal representation primarily determines whether planning scales: as dependency graphs grow from 5 to 100 actions, Planner collapses from 96% to 5% plan accuracy and PDDL2.1 Formalizer from 13% to 0%, while CP-SAT Formalizer averages 94% and still achieves 83% at 100 actions. Faithfulness diagnostics show that PDDL2.1's predicate-based planning representation becomes brittle compared to general constraint satisfaction programs, when LLMs must keep predicates, effects, and goals consistent. Execution-time updates of planning constraints further degrade performance sharply (Planner 23.9%, PDDL2.1 0.7%, CP-SAT 46.1%), but a state-aware repair strategy that updates only event-induced constraints recovers CP-SAT Formalizer to 84.5%.

Figures

Figures reproduced from arXiv: 2606.00981 by the authors.

Figure 1
Figure 1. Overview of LLM-based asynchronous plan [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Three asynchronous planning settings covered [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Plan accuracy on AsyncPlan-XXL as the dependency-graph size grows from 5 to 100 actions. Lines show the mean across Gemini 3 Flash and DeepSeek-V4-Flash; shaded bands show min/max. edge, Online Robo Challenge is the first bench￾mark to combine both: LLM-based asynchronous planning under execution-time events that revise constraints, durations, or resource availability. It contains seven 20-instance subsets ( [PITH_… view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: Plan accuracy by split on Robo Challenge (top) and Online Robo Challenge (bottom), averaged across [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Average plan accuracy on Robo Challenge (offline), Online Robo Challenge with one-shot re￾formalization, and Online Robo Challenge with state￾aware CP-SAT repair, averaged across four LLMs. Per￾model breakdowns are in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Overview of the three LLM planning inter [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Plan accuracy on AsyncPlan-XXL by graph size (top), and dominant failure modes by step range for [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Prompt template for Planner on AsyncHow and AsyncPlan-XXL. [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]
Figure 9
Figure 9. Figure 9: Prompt template for the PDDL2.1 Formalizer on AsyncHow and AsyncPlan-XXL. [PITH_FULL_IMAGE:figures/full_fig_p022_9.png]
Figure 10
Figure 10. Figure 10: Prompt template for the CP-SAT Formalizer on AsyncHow and AsyncPlan-XXL. [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11: Syntax retry prompt for the PDDL2.1 Formalizer. [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]
Figure 12
Figure 12. Figure 12: Validation retry prompt for the CP-SAT Formalizer. [PITH_FULL_IMAGE:figures/full_fig_p023_12.png]
Figure 13
Figure 13. Figure 13: Prompt used in the second stage of the AsyncPlan-XXL generation pipeline, where abstract DAGs are [PITH_FULL_IMAGE:figures/full_fig_p024_13.png]
Figure 14
Figure 14. Figure 14: Prompt template for Planner on Robo Challenge. [PITH_FULL_IMAGE:figures/full_fig_p024_14.png]
Figure 15
Figure 15. Figure 15: Prompt template for the PDDL2.1 Formalizer on Robo Challenge. [PITH_FULL_IMAGE:figures/full_fig_p025_15.png]
Figure 16
Figure 16. Figure 16: Prompt template for the CP-SAT Formalizer on Robo Challenge. [PITH_FULL_IMAGE:figures/full_fig_p026_16.png]
Figure 17
Figure 17. Figure 17: Shared online execution context appended to Online Robo Challenge prompts. [PITH_FULL_IMAGE:figures/full_fig_p026_17.png]
Figure 18
Figure 18. Figure 18: Prompt template for Planner on Online Robo Challenge. [PITH_FULL_IMAGE:figures/full_fig_p027_18.png]
Figure 19
Figure 19. Figure 19: Prompt templates for the PDDL and CP-SAT Formalizers on Online Robo Challenge. [PITH_FULL_IMAGE:figures/full_fig_p027_19.png]

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Reference graph

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Show all 81 references
  1. [9]

    Include one action for every listed step

  2. [10]

    step1","step2

    Use ids exactly"step1","step2", . . . , matching the original step numbers

  3. [11]

    Convert every duration to seconds

  4. [12]

    before"is the step that must finish first

    Include every direct ordering constraint as a dependency. 5."before"is the step that must finish first;"after"is the step that starts later. 6.final_answer_secondsis your computed shortest possible completion time under infinite resources

  5. [13]

    Figure 8: Prompt template for Planner on AsyncHow and AsyncPlan-XXL

    Do not include markdown, prose, or explanation. Figure 8: Prompt template for Planner on AsyncHow and AsyncPlan-XXL. Prompt for PDDL2.1 Formalizer System prompt:You are a PDDL expert. Given an asynchronous planning problem, write the domain and problem files in minimal PDDL2.1...

  6. [14]

    Use only :durative-actions in :requirements; do not use :typing, :negative-preconditions, :adl, or :disjunctive-preconditions

  7. [15]

    Use positive _pending predicates in conditions, and delete them only in effects

    Never use(not ...) in action preconditions. Use positive _pending predicates in conditions, and delete them only in effects

  8. [16]

    Do not include:typesor:objects; actions take no parameters

    Declare all predicates before use. Do not include:typesor:objects; actions take no parameters

  9. [17]

    Use(:durative-action ...)with exactly one:duration, one:condition, and one:effect

  10. [18]

    Use(at start ...),(at end ...), or(over all ...)inside conditions and effects

  11. [19]

    Semantic rules

    Initialize all_pendingpredicates in the problem:init. Semantic rules

  12. [20]

    Every action must consume its own(X_pending) at start, produce its own(X_done) at end, and require all direct predecessors’_donepredicates as(at start ...)conditions

  13. [21]

    The graph is a DAG, not a linear chain: if a step has multiple predecessors, enforce all of them as an AND-join

  14. [22]

    The problem goal must include all_donepredicates, one per action, so the planner cannot skip steps

  15. [23]

    Do not introduce one-second placeholder actions

    Every action duration must be exactly the duration stated in the problem, converted to seconds. Do not introduce one-second placeholder actions

  16. [24]

    after”, “once

    The number of durative actions must exactly equal the number of listed steps. Dependency analysis.For each step, ask what must be fully completed before this step can start. Check explicit cues such as “after”, “once”, “following”, and numbered constraints. A missing predecess...

  17. [25]

    Each numbered step in the problem becomes exactly one action

  18. [26]

    Useaction="task"for every action

  19. [27]

    ,stepNbased on the step numbers in the problem text

    Use the exact idsstep1,step2, . . . ,stepNbased on the step numbers in the problem text

  20. [28]

    Use item values identical to the action ids:step1,step2, . . . ,stepN

  21. [29]

    Duration must be the integer number of seconds for that step

  22. [30]

    Do not add extra dependencies

    Add a dependency only when the problem states that one step must happen before another. Do not add extra dependencies

  23. [31]

    Do not add stations, robots, or resources

  24. [32]

    Output only valid JSON with keysactionsanddependencies

  25. [33]

    User prompt: Translate this planning problem into a CP-SAT scheduling JSON spec

    Before finishing, verify that every step appears exactly once, every dependency endpoint exists, durations are integer seconds, and there are no duplicate actions. User prompt: Translate this planning problem into a CP-SAT scheduling JSON spec. Problem: {question} The problem ...

  26. [34]

    Analyze the error message and identify all issues; there may be more than one

  27. [35]

    Think step by step about how each issue relates to the PDDL syntax or semantics

  28. [36]

    Figure 11: Syntax retry prompt for the PDDL2.1 Formalizer

    Fix all issues and return the corrected domain and problem PDDL. Figure 11: Syntax retry prompt for the PDDL2.1 Formalizer. CP-SAT Formalizer Retry Prompt Your previous scheduling JSON could not be parsed or validated. Error: {error} Please return a corrected JSON object only....

  29. [37]

    Keep the task title exactly as given

  30. [38]

    Keep the exact same number of steps

  31. [39]

    Copy all ordering constraints verbatim, with the same step numbers and wording

  32. [40]

    Copy the final question line verbatim

  33. [41]

    For each step, add a concrete activity-specific name and a reasonable duration in parentheses

  34. [42]

    The step names should form a coherent, realistic workflow for the task

  35. [43]

    Use diverse but plausible durations; not every step should use the same unit or take the same amount of time

  36. [44]

    The ordering constraints should make logical sense with the step names

  37. [45]

    No commentary, markdown fences, or extra text

    Output only the rewritten problem. No commentary, markdown fences, or extra text. User prompt: Here is an abstract asynchronous planning problem: {abstract_planning_question} Figure 13: Prompt used in the second stage of the AsyncPlan-XXL generation pipeline, where abstract DA...

  38. [47]

    Use exact item names and, when present, exact robot names from the task

  39. [48]

    Independent actions may run in parallel, but an item cannot receive two actions at once

  40. [49]

    Respect action preconditions: for example, marinate requires cut, mash requires boiled, and task-specific cut- before-fry or marinate-before-grill requirements must be obeyed

  41. [50]

    Respect station capacities and robot exclusivity

  42. [51]

    Stack items only after all required processing is complete, and stack in the required bottom-to-top order

  43. [52]

    Enforce all temporal wait constraints and deadlines

  44. [53]

    For reward-maximization tasks, choose a feasible candidate subset under the deadline and inventory limits

  45. [54]

    User prompt: Produce a temporal plan for the following cooking task

    Output only plan lines; no explanation or markdown. User prompt: Produce a temporal plan for the following cooking task. {nl} IMPORTANT – use these EXACT item names (with underscores) in your plan: {item_names} If robots are listed in the task, include the robot argument in ev...

  46. [55]

    Use a(stackable <item>)predicate to indicate that an item is ready to be stacked

  47. [56]

    Generate one separate durative action per item in the stack order, namedstack_<item>

  48. [57]

    Interface contract

    Encode each station capacity with a<station>_free predicate: an action requires it at start, deletes it at start, and restores it at end. Interface contract

  49. [58]

    Executable base action names must be onlygrill,cut,fry,boil,toast,marinate,mash, andstack

  50. [59]

    If an item-specific ground action is needed, name it<base_action>_<exact_item_name>; never invent names such ascook,prepare,grill_raw, orfry_generic

  51. [60]

    If robots are present, executable actions must include a robot argument and must require and release(robot_free ?r)

  52. [61]

    PDDL rules

    Use exact item and robot names everywhere; never shorten names or insert underscores before numeric suffixes. PDDL rules

  53. [62]

    Use (:requirements :durative-actions :typing) and declare type item; also declare robot when robots are listed

  54. [63]

    Declare predicates for item states, stackable, stacked, ready, station-free predicates, and optional robot-free predicates

  55. [64]

    Processing actions consume their required input state and produce their output state; task-specific chains must update both conditions and effects, e.g., cut-before-fry uses(cut ?i), not(raw ?i)

  56. [65]

    Stack actions require(stackable <item>)and, except for the first stack item,(stacked <previous_item>)

  57. [66]

    Temporal waits are encoded with planner-onlywait_*durative actions plus completion and lag predicates

  58. [67]

    The goal includes all required processed states and all stacked items in the final stack order

  59. [68]

    domain_pddl

    Do not use negative preconditions,or, orwhen. Output format.Return only valid JSON: {"domain_pddl": "<full domain PDDL>", "problem_pddl": "<full problem PDDL>"} User prompt: Translate the following cooking task into PDDL2.1. {nl} IMPORTANT – use these EXACT item names in all P...

  60. [69]

    Allowed actions aregrill,cut,fry,boil,toast,marinate,mash, andstack

  61. [70]

    Allowed non-stack stations aregrill,cutting_board,fryer,boiler,toaster, andmarinator

  62. [71]

    Each action id must be <action>_<item>; dependency endpoints must use existing action ids

    Use exact item identifiers. Each action id must be <action>_<item>; dependency endpoints must use existing action ids

  63. [72]

    Include all processing actions required to reach required states, and include stack actions only for items in the final stack order

  64. [73]

    Add dependencies for all multi-step chains, item-final-processing to stack, stack order, and explicit temporal waits

  65. [74]

    Do not add resource-order dependencies; CP-SAT handles station conflicts

  66. [75]

    If robots are listed, includeeligible_robotsfor every action

  67. [76]

    mode": "schedule

    For candidate-reward tasks, output an optimization model rather than making every candidate action mandatory. Output format.For ordinary scheduling tasks, return: {"mode": "schedule", "actions": [...], "dependencies": [...]} For reward optimization tasks, return: {"mode": "opt...

  68. [77]

    Times are relative to now; the first new action can start at0.000

  69. [78]

    Output only future actions that have not started yet

  70. [79]

    Do not repeat completed or ongoing actions; ongoing actions finish automatically

  71. [80]

    Respect remaining station occupancy, robot occupancy, action preconditions, deadlines, and inventory limits

  72. [81]

    Use exact item and robot names from the prompt

  73. [82]

    delta": {

    For optimization episodes, choose a feasible remaining subset under the deadline. User prompt: Current time: {now} seconds Plan the remaining work for this online cooking episode. {nl} Exact item names: {item_names} Already completed before now: {completed} Committed ongoing a...

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Reviewed June 28, 2026 · model on record in the stance chip above.