Fill algorithm
Algorithms AIMech:FillAlgorithm DRAFT
An idealized finite constraint-satisfaction search algorithm that takes any strictly cost-reducing single-variable change when available and otherwise increases only the stored cost of the current non-solution assignment.
Identity Notes & Concept Scope
This is Morris’s named Fill algorithm, introduced to distinguish state-specific cost lifting from Breakout’s shared nogood reweighting. It is not flood fill, image inpainting, or LRTA*. Fill permits any lower-cost neighbor, while LRTA* selects a minimum estimated path-cost successor and backs up its value even away from local minima. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 313 preceding native IDs/names/aliases. Full-checkout fixed-string searches included ignored and hidden files in worktree and main, returning 24 and 24 lines respectively. All 24 unique lines were inspected, and the sorted checkout hit sets were identical: prior leads, neighboring Breakout descriptions and their saved reviews/ledgers, not existing candidate records. Seven exact AIO CLASS nodes with scoped synonyms/comments and outgoing edges and four full native neighboring records were inspected. Absence is bounded to this snapshot and semantic neighborhood.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
Initialize a modifiable cost for complete assignments using the original constraint-violation cost. Test the current assignment for satisfaction. If a single-variable change strictly reduces its stored cost, take any such change; otherwise increase the stored cost of that current assignment alone and continue. Costs of other assignments do not change as a side effect. Retain raised costs for later revisits. Figure 3 specifies an increase without fixing its magnitude; the finite-CSP completeness proof relies on repeated lifts of an endlessly visited minimum eventually exceeding every fixed neighboring cost. Positive unit increments satisfy that intended lifting property. The theorem concerns eventual arrival at a solution when one exists on the finite complete-assignment space with the stated single-variable adjacency.
⚠️ Curated Limitations & Negative Results
- The source’s theorem is not a finite-budget guarantee or an unsatisfiability decision procedure. Restricting moves so a solution is unreachable, or replacing the finite assignment space with an infinite one, is outside that theorem.
- Figure 3 does not prescribe a numerical increment. Curator qualification: arbitrary positive increments with a bounded cumulative sum need not satisfy the proof’s unbounded-lifting step; completeness should not be transferred to such an implementation without a separate argument.
- State-specific costs must survive revisits. They can require storage growing with encountered local minima; the compact shared-nogood representation used by Breakout changes the method and does not inherit Fill’s theorem.
- The constraint-violation score need not be an admissible estimate of distance to a solution. The method is not a shortest-path optimality algorithm. No runtime advantage, numerical experiment or author implementation is asserted.
Artificial Intelligence Ontology (AIO) Grounding
Explicit AIO Snapshot Assessment: No Match
Rationale: No suitable AIO counterpart was established for this basic state-space search procedure in the inspected snapshot and neighborhood. Shared graph, reasoning or heuristic words do not justify a model/task mapping.
Search Scope: All 442 pinned AIO labels/scoped synonyms and 313 preceding maintained IDs/names/aliases; ignored/hidden text in both full checkouts; semantic label search for search, planning, heuristic, path, traversal, symbolic, reasoning, graph, reinforcement and learning-task terminology; seven exact AIO CLASS nodes and four complete native neighbors.
| Examined AIO Candidate | Rejection Reason |
|---|---|
AIO:GraphLanguageModel
|
Operating on a state-space graph does not make this procedure a language model over graph representations. |
AIO:ReasoningLLM
|
The target is a language model with reasoning during language tasks, not a general path or constraint search algorithm. |
AIO:NeuroSymbolicLLM
|
This procedure does not require neural language modeling or a neuro-symbolic language-model architecture. |
AIO:MachineLearningTask
|
This basic single-search procedure adjusts search bookkeeping; it does not require learning a reusable predictor from multiple problem-solving trials. The separately curated LRTA* extension explicitly does that. |
AIO:MathematicalFunction
|
The algorithm uses and updates a cost function; it is not identical to the mathematical function itself. |
AIO:ReinforcementLearning
|
Search, revisitation and adaptive costs alone do not identify the basic procedure with a learning task balancing exploration and exploitation. Multi-trial heuristic learning is separately represented. |
AIO:TrainingStrategy
|
This algorithm does not require preprocessing or training a machine-learning model. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Paul Morris
|
primary paper
full_text
|
sha256:9f853b683140…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T15:04:45Z
Updated: 2026-10-11T15:04:45Z
Source File:
data/curated/FillAlgorithm.yaml