Disjoint Partial Enumeration without Blocking Clauses

Armin Biere; Giuseppe Spallitta; Roberto Sebastiani

arxiv: 2306.00461 · v4 · submitted 2023-06-01 · 💻 cs.LO

Disjoint Partial Enumeration without Blocking Clauses

Giuseppe Spallitta , Roberto Sebastiani , Armin Biere This is my paper

Pith reviewed 2026-05-24 08:35 UTC · model grok-4.3

classification 💻 cs.LO

keywords disjoint model enumerationAllSATblocking clausesCDCLchronological backtrackingimplicant shrinkingSAT solvingpartial models

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The pith

A method integrates CDCL, chronological backtracking, and implicant shrinking to enumerate disjoint partial models without blocking clauses.

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

Standard approaches to finding all disjoint propositional models add blocking clauses to prevent repeats, but these clauses consume memory and slow down propagation. The paper shows how to combine conflict-driven clause learning, chronological backtracking, and techniques to shrink models into implicants. This combination lets the solver list partial models that are disjoint without ever inserting blocking clauses. Experiments indicate the new method uses less memory and runs faster than clause-based alternatives. A reader would care because many verification and synthesis tasks rely on enumerating models efficiently.

Core claim

The central claim is that integrating Conflict-Driven Clause-Learning (CDCL), Chronological Backtracking (CB), and Implicant Shrinking enables the enumeration of disjoint partial models without the need for blocking clauses, while maintaining correctness and improving performance over traditional methods that rely on blocking clauses.

What carries the argument

The integration of CDCL for learning, CB for search order, and implicant shrinking to produce partial models, which together replace the role of blocking clauses in ensuring disjointness.

If this is right

Memory consumption decreases because no blocking clauses are stored.
Unit propagation speeds up without the overhead of many clauses.
The approach handles partial models naturally through shrinking.
Performance gains appear in experimental comparisons on standard benchmarks.

Where Pith is reading between the lines

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

This could extend to other SAT-based enumeration problems where clause management is a bottleneck.
Future solvers might adopt similar combinations for related tasks like prime implicant generation.
The method might scale to larger instances where blocking clauses cause out-of-memory issues.

Load-bearing premise

Combining clause learning during search, ordered backtracking, and shrinking of found models into smaller ones can list all unique partial solutions without repeats or omissions.

What would settle it

Running both the new method and a blocking-clause baseline on a small satisfiable formula and checking if the sets of enumerated partial models match exactly, or measuring if the new method uses more time or memory on large instances.

read the original abstract

A basic algorithm for enumerating disjoint propositional models (disjoint AllSAT) is based on adding blocking clauses incrementally, ruling out previously found models. On the one hand, blocking clauses have the potential to reduce the number of generated models exponentially, as they can handle partial models. On the other hand, the introduction of a large number of blocking clauses affects memory consumption and drastically slows down unit propagation. We propose a new approach that allows for enumerating disjoint partial models with no need for blocking clauses by integrating: Conflict-Driven Clause-Learning (CDCL), Chronological Backtracking (CB), and methods for shrinking models (Implicant Shrinking). Experiments clearly show the benefits of our novel approach.

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 integrates CDCL, chronological backtracking, and implicant shrinking to enumerate disjoint partial models without blocking clauses, addressing a known efficiency issue but with thin experimental detail.

read the letter

The main points are that the authors integrate CDCL, chronological backtracking, and implicant shrinking to enumerate disjoint partial models without blocking clauses, and they claim experiments back this up. This is new as a way to handle the enumeration while avoiding the downsides of many blocking clauses on memory and propagation speed. The paper does well at explaining why blocking clauses become a problem and how these other components can substitute for them in maintaining disjointness. The soft spot is the lack of experimental details; the abstract asserts benefits but does not describe the setup, baselines, or quantitative results, so it's difficult to assess the practical impact or reproducibility. If the full paper includes proofs of correctness and clear comparisons, that would address this. Nothing in the description points to an internal inconsistency or violated assumption. This paper is for SAT researchers focused on AllSAT and enumeration techniques, particularly those in computer-aided verification. It deserves peer review to get the details checked and see if the approach scales as hoped.

Referee Report

1 major / 0 minor

Summary. The paper proposes a new algorithm for enumerating disjoint partial propositional models (disjoint AllSAT) that avoids blocking clauses entirely. It integrates Conflict-Driven Clause-Learning (CDCL), Chronological Backtracking (CB), and Implicant Shrinking to maintain disjointness while mitigating the memory consumption and unit-propagation slowdowns caused by large numbers of blocking clauses. The central claim is that this integration is correct and that experiments demonstrate clear performance benefits over clause-based methods.

Significance. If the integration preserves correctness and the claimed performance gains hold, the work would be a meaningful contribution to AllSAT and model-enumeration algorithms. Avoiding blocking clauses addresses a well-known practical bottleneck; the explicit combination of CDCL, chronological backtracking, and shrinking is a concrete technical idea that could be adopted in solvers. No machine-checked proofs or parameter-free derivations are mentioned, but the algorithmic novelty itself is a strength if substantiated.

major comments (1)

[Abstract / Experimental Evaluation] Abstract and Experimental Evaluation: the claim that 'Experiments clearly show the benefits of our novel approach' is load-bearing for the central contribution, yet the manuscript provides no description of benchmarks, baselines (e.g., standard blocking-clause AllSAT solvers), metrics (runtime, number of models, memory), statistical analysis, or error bars. Without these details it is impossible to assess whether the data support the performance assertions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed review and the opportunity to clarify the experimental claims. We address the single major comment below.

read point-by-point responses

Referee: [Abstract / Experimental Evaluation] Abstract and Experimental Evaluation: the claim that 'Experiments clearly show the benefits of our novel approach' is load-bearing for the central contribution, yet the manuscript provides no description of benchmarks, baselines (e.g., standard blocking-clause AllSAT solvers), metrics (runtime, number of models, memory), statistical analysis, or error bars. Without these details it is impossible to assess whether the data support the performance assertions.

Authors: We agree that the current manuscript does not provide adequate detail on the experimental setup. The Experimental Evaluation section will be expanded in the revision to describe the benchmarks (including the specific instance suites and their characteristics), the baseline solvers (standard blocking-clause AllSAT implementations), the metrics collected (runtime, number of models, memory consumption), and any statistical analysis or error bars. The abstract claim will be retained only after these supporting details are added. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents a novel algorithmic integration of CDCL, chronological backtracking, and implicant shrinking to enumerate disjoint partial models without blocking clauses, with the central claim resting on experimental validation of performance benefits. No equations, self-definitions, fitted parameters renamed as predictions, or load-bearing self-citations appear in the provided description. The approach is self-contained as a practical method whose correctness and efficiency are assessed externally via benchmarks rather than reducing to its own inputs by construction. This is the expected outcome for an empirical algorithms paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the integration of standard SAT techniques works correctly for the new use case of blocking-clause-free disjoint partial enumeration, plus the validity of the experimental results. No free parameters or invented entities are apparent from the abstract.

axioms (1)

domain assumption The combination of CDCL, chronological backtracking, and implicant shrinking preserves the disjointness property for partial models without blocking clauses.
This is the core assumption enabling the no-blocking-clause approach as stated in the abstract.

pith-pipeline@v0.9.0 · 5638 in / 1210 out tokens · 26278 ms · 2026-05-24T08:35:59.356721+00:00 · methodology

discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

We propose a new approach that allows for enumerating disjoint partial models with no need for blocking clauses by integrating: Conflict-Driven Clause-Learning (CDCL), Chronological Backtracking (CB), and methods for shrinking models (Implicant Shrinking).

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