arxiv: 2605.13185 · v1 · submitted 2026-05-13 · 💻 cs.FL · cs.MA

Recognition: no theorem link

Decoupled Planning for Multiple Omega-Regular Objectives

Guy Avni, Kaushik Mallik, K. S. Thejaswini, Suman Sadhukhan, Thomas A. Henzinger

Pith reviewed 2026-05-14 01:35 UTC · model grok-4.3

classification 💻 cs.FL cs.MA

keywords omega-regular objectivesdecoupled planningpolicy compositionBuchi objectivesco-Buchi objectivesparity objectivesschedulers

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The pith

Agents satisfy multiple omega-regular objectives on a graph through independent local policies composed by a scheduler if they follow pre-agreed conventions specific to each objective class.

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

This paper develops a decoupled approach to planning paths that meet several omega-regular conditions at once. Separate agents each pick a policy for one condition, and a scheduler that ignores the graph puts the policies together into one path. The key result is that pre-agreed conventions on how agents respond when scheduled can make the composition work for non-safety objectives. For the main subclasses, the paper identifies exactly how much scheduler information each type needs: none for Büchi, presence information for co-Büchi, and agent identity for parity.

Core claim

The conjunction of omega-regular objectives can be realized by composing independent finite-memory policies via an oblivious scheduler when agents adhere to minimally restrictive conventions chosen for the objective class. Büchi objectives permit universal composition without scheduler communication, co-Büchi objectives require only knowledge of whether the agent was scheduled, and parity objectives require knowledge of which agent was scheduled.

What carries the argument

The conventions: simple restrictions on policy behavior agreed upon in advance that ensure the scheduler's composition satisfies every objective.

If this is right

Büchi objectives admit universal composition of finite-memory policies without any scheduler communication.
Co-Büchi objectives can be satisfied with only knowledge of whether the agent was scheduled.
Parity objectives require additional knowledge of which agent was scheduled.
Safety objectives cannot be handled in a fully decentralized way and need a protocol to synchronize on maximal safe actions.

Where Pith is reading between the lines

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

Modular design of controllers for multiple tasks becomes possible without sharing full information about the environment.
This could extend to other classes of objectives by defining appropriate conventions for each.
Applications in autonomous systems might allow tasks to be assigned to separate modules that coordinate only through the scheduler.

Load-bearing premise

All agents agree in advance on the conventions, and the conjunction of the objectives is realizable on the graph.

What would settle it

Find a graph where the joint objectives are realizable but any set of policies following the stated conventions for Büchi objectives produces a violating path under a fair stochastic scheduler.

Figures

Figures reproduced from arXiv: 2605.13185 by Guy Avni, Kaushik Mallik, K. S. Thejaswini, Suman Sadhukhan, Thomas A. Henzinger.

**Figure 3.** Figure 3: Decoupling planning using a convention Conv [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

**Figure 4.** Figure 4: A graph with two coBüchi objectives given by bad states v1,1 (Red) and v1,2 (Blue). Red edges are chosen by π1 and Blue edges by π2. Consider a strongly-connected graph G, a stochastic scheduler σ, and a co-Büchi objective φ given by a set of “bad” states B. Let CB denote the set of “good” simple cycles in G that are disjoint from B. A policy π ∈ Convco-Büchi(G, σ, φ) proceeds as follows. It randomly ch… view at source ↗

**Figure 5.** Figure 5: This figure is redrawn for convenience. Red is module 1’s Büchi state, and [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗

**Figure 6.** Figure 6: Graph G used in the proof of Theorem 5. Figure is redrawn from [PITH_FULL_IMAGE:figures/full_fig_p027_6.png] view at source ↗

read the original abstract

We study the problem of generating paths on a graph that satisfy a collection of {\omega}-regular objectives. We propose a decoupled framework in which each objective is assigned to an independent agent that selects a local policy, while a scheduler -- oblivious to the graph and objective -- dynamically composes these policies into a single path. We ask when such a composition satisfies all objectives, assuming their conjunction is realizable. The framework enables modular policy design but raises fundamental compositional challenges. We show that even extremely fair deterministic schedulers do not ensure correctness, and that stochastic schedulers, while necessary, are insufficient without coordination. For safety objectives, we demonstrate that fully decentralized implementations are impossible, and we introduce a protocol for synchronizing on maximal safe actions. For non-safety objectives, we introduce conventions -- simple, a priori restrictions agreed upon before the graph or objectives are revealed -- that guarantee satisfaction of all objectives when followed by all agents. We characterize minimally restrictive conventions for major subclasses of {\omega}-regular objectives. In particular, B\"uchi objectives admit universal composition of finite-memory policies without scheduler communication; co-B\"uchi objectives require only knowledge of whether the agent was scheduled; and parity objectives additionally require knowledge of which agent was scheduled.

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.

Desk Editor's Note private letter to a colleague

The paper gives a decoupled agent model for multi-objective omega-regular synthesis on graphs, with concrete characterizations of minimal conventions needed for Büchi, co-Büchi, and parity cases.

read the letter

The core contribution is a framework that splits a set of omega-regular objectives across independent agents, each choosing its own policy, while a scheduler composes them into one path. The authors show that deterministic schedulers, even very fair ones, fail to guarantee all objectives are met, and that stochastic schedulers still need extra coordination. They then introduce a priori conventions that supply exactly the coordination required for different objective classes. Büchi objectives work with universal finite-memory composition and no scheduler communication at all. Co-Büchi needs only knowledge of whether the agent was scheduled. Parity adds knowledge of which agent was scheduled. For safety objectives they give an explicit synchronization protocol on maximal safe actions. These distinctions look useful because they turn a general composition problem into something modular and class-specific. The work builds directly on standard automata and realizability assumptions without obvious circularity. The main limitation is the standing assumption that the conjunction of objectives is already realizable on the graph; the framework does not create realizability from scratch. The conventions must also be agreed before the graph or objectives are known, which is a real restriction but is stated clearly. Without the full proofs it is hard to check the automata constructions in detail, but the abstract claims line up consistently with the stated assumptions. This is aimed at researchers in formal synthesis and graph games who already work with omega-regular specifications. A reader comfortable with Büchi automata and memoryless strategies will find the characterizations directly usable. The paper deserves serious peer review because the modular approach and the minimal-convention results are specific enough to be checked and potentially applied.

Referee Report

1 major / 2 minor

Summary. The paper introduces a decoupled framework for generating paths satisfying multiple ω-regular objectives on a graph, assigning each objective to an independent agent that selects a local policy; these are dynamically composed by a scheduler oblivious to the graph and objectives. Assuming the conjunction is realizable, it shows deterministic schedulers (even fair ones) fail to guarantee correctness, stochastic schedulers require additional coordination, and a priori conventions suffice for non-safety objectives. It characterizes minimally restrictive conventions: Büchi objectives allow universal finite-memory policy composition without scheduler communication; co-Büchi require only knowledge of whether the agent was scheduled; parity require additionally which agent was scheduled. A synchronization protocol is given for safety objectives.

Significance. If the characterizations and constructions hold, the work provides a valuable modular approach to multi-objective synthesis in automata theory and verification, reducing the need for centralized control while identifying the precise coordination required per objective class. The explicit use of conventions as a minimal, pre-agreed mechanism is a strength, as is the separation of scheduler obliviousness from agent-level knowledge.

major comments (1)

[Main results on Büchi objectives] The central claim that Büchi objectives admit universal composition of finite-memory policies without scheduler communication (abstract and main results) rests on unverified steps in the provided summary; the manuscript must include the explicit policy construction and proof that finite memory suffices independently of the scheduler for all realizable conjunctions.

minor comments (2)

[Framework section] Clarify the precise definition of 'oblivious to the graph and objective' for the scheduler and how it interacts with the stochastic requirement, perhaps with a formal definition in the framework section.
[Safety objectives subsection] The safety objective protocol is mentioned but its integration with the convention-based approach for non-safety cases could be cross-referenced more explicitly for completeness.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of the work's significance, and recommendation for minor revision. We address the major comment below and will strengthen the manuscript accordingly.

read point-by-point responses

Referee: [Main results on Büchi objectives] The central claim that Büchi objectives admit universal composition of finite-memory policies without scheduler communication (abstract and main results) rests on unverified steps in the provided summary; the manuscript must include the explicit policy construction and proof that finite memory suffices independently of the scheduler for all realizable conjunctions.

Authors: We agree that the explicit policy construction and a fully detailed proof are required to substantiate the claim. The full manuscript presents the construction for Büchi objectives in Section 4.2, including the definition of the finite-memory policies and the argument that their composition satisfies the conjunction independently of the scheduler. However, we acknowledge that some verification steps were presented at a high level. In the revised version we will expand this section with a complete, self-contained proof that explicitly constructs the composed policy, verifies memory finiteness, and shows correctness for every realizable conjunction under arbitrary schedulers. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claims rest on explicit assumptions (conjunction of objectives is realizable; agents pre-agree on class-specific conventions) and standard results from automata theory and realizability. No derivation reduces a prediction or theorem to a fitted parameter, self-definition, or self-citation chain. The characterizations for Büchi, co-Büchi, and parity objectives are derived from the framework's definitions of policies, schedulers, and conventions without circular reduction. The work is self-contained against external benchmarks in omega-regular games.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard automata theory for omega-regular objectives and the assumption that the conjunction is realizable; no free parameters or new entities are introduced.

axioms (2)

standard math Omega-regular objectives are recognized by automata on infinite words
Used to define the objectives and realizability throughout.
domain assumption Conjunction of objectives is realizable when a satisfying path exists
Stated explicitly to focus analysis on composition rather than existence.

pith-pipeline@v0.9.0 · 5531 in / 1286 out tokens · 68211 ms · 2026-05-14T01:35:07.269893+00:00 · methodology

discussion (0)

Reference graph

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