---
title: "algorithm-longest-common-subsequence-tests"
description: "Mova code model of algorithms/src/longest_common_subsequence/tests.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/longest_common_subsequence/tests.rs.groupant/"
---
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# algorithm-longest-common-subsequence-tests

The groupant beside algorithms/src/longest_common_subsequence/tests.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

## Facts

- **kind:** groupant
- **status:** partial source derived instance
- **source:** [`algorithms/src/longest_common_subsequence/tests.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/longest_common_subsequence/tests.rs)
- **source SHA-256:** `ab71a32fd5dfb5dc…`
- **repository folder:** [`algorithms/src/longest_common_subsequence/tests.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/longest_common_subsequence/tests.rs.groupant)
- **repository commit:** `855da7bd4a7b`

> **Implementation material.** A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.

## Components

| component | label | where |
|---|---|---|
| **approximant** | bounded checked | [Forward](#forward) |
| **ast** | partial | `syntax.json` |
| **cost** | symbolic unmeasured | [Cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | source derived | [Invariant](#invariant) |
| **tests** | bounded executed | [evidence](#evidence) |

## Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

| id | type | label | where |
|---|---|---|---|
| `nonbehavior` | behavior_complement | partial source derived | [nonbehavior](#nonbehavior) |
| `preimages` | reverse_reconstruction | partial source derived | [preimages](#preimages) |
| `oracle` | observational_equivalence | partial source derived | [oracle](#oracle) |
| `relations` | metamorphic_relation | partial source derived | [relations](#relations) |
| `sensitivity` | counterfactual_model | partial source derived | [sensitivity](#sensitivity) |

## Model text


### descriptant

#### longest_common_subsequence tests.rs

Independent exponential oracle plus metamorphic and boundary checks. Source is authoritative; sidecar models and syntax are partial. Models compose recurrence, bounds and public result; tests observe this composition rather than establish a universal proof. No approximate execution profile is supplied because this API promises exact results; finite evidence is not an analytical error guarantee.

Epoch 2026-10-30: prospective cost and invariants retained in implementation prospective.md. The reverse models retain ambiguous input fibers and separate behavior exclusions from reconstruction. No timing optimization claimed.

### model

## longest_common_subsequence tests.rs model

### Forward

Execute deterministic finite fixtures with independent exponential oracle and production-linked relational assertions. Passing supports only the observed domain.

### Invariant

Oracle enumerations are finite and include empty choices. Assertions inspect actual production returns. No random generator, network or imported implementation.

### Cost

Bounded exponential test oracle; suitable only for small fixtures. Production cost is modeled separately.

### nonbehavior

Type: behavior_complement. A passing outcome excludes observed disagreements on enumerated fixtures and oracle comparisons; untested behaviors remain admitted. This relation describes exclusions within the finite observation universe.

### preimages

Type: reverse_reconstruction. A passing report admits all implementations agreeing on these fixtures, including incorrect ones elsewhere. A failed assertion constrains a mismatch at its fixture, not unique source reconstruction.

### oracle

Type: observational_equivalence. Enumerate all subsequences by bitmask and scan the second input; compare 63 squared binary-word pairs through length five. The oracle does not share the rolling recurrence.

### relations

Type: metamorphic_relation. Tests observe symmetry, identity, simultaneous reversal, common fresh-symbol append, one-sided bounds, generic values and a nonunique preimage counterexample.

### sensitivity

Type: counterfactual_model. Changing the equality recurrence from diagonal+1 to diagonal is a compiled production fault that the independent oracle must reject. Other faults remain unproven.

### evidence

#### Evidence epoch 2026-10-30

Final source validation: two debug and two release executions of the complete mova-algorithms package passed 176 unit tests and one doctest each. Nine new tests belong to these two algorithms (four LCS, five scheduling). Sorted named test outcomes were identical across all four runs; elapsed time and build chatter were excluded. Normalized outcome SHA-256: c38c9be833de92508d6cd6304a57c36c196c4c4ef57561fa9c7f361dd7816255.

LCS independent oracle enumerates subsequences of each first argument and scans the second, checking all 63 squared binary-word pairs through length five (3,969 pairs). Scheduling independently enumerates subsets and pairwise compatibility for all 5,461 arrays through length six over four item choices. Metamorphic tests include explicit input-fiber ambiguity, boundary and invalid-input cases. Allocator exhaustion and unreachable allocated-slice dimension/weight overflow cases were not executed.

Strict Clippy all-targets with -D warnings passed. rustfmt --check passed for all four owned Rust files. Installed mova-modelcheck syntax ran twice per source and produced byte-identical projections. Syntax is partial: macros and semantic typing are not expanded.

Compiled production negative control: replace diagonal + 1 by diagonal; real tests fail. Mutant log SHA-256 06baa16dba164cddf913d8455300a11c29c12bbb561def59459eb3576c3c5346. Original source restored before final repeated runs.

Artifacts live under $MOVA_DATA/runs/octopus-wave4-dynamic-2026-10-30. A temporary local lib declaration was used for package integration tests and restored. Registry-entry copies are supplied for main-instance integration; shared registry hierarchy checks remain the integrator's responsibility. These observations establish bounded correctness evidence and sensitivity to the named fault, not a proof or benchmark gain.