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algorithm-offline-dynamic-connectivity-tests

The groupant beside algorithms/src/offline_dynamic_connectivity/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

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

componentlabelwhere
approximantpartialForward
astpartialsyntax.json
costconditionalCost
descriptantpresentdescriptant
invariantpartialInvariant
testsbounded executedevidence

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.

idtypelabelwhere
behavior_complementbehavior_complementpartial relational specificationbehavior_complement
reverse_reconstructionreverse_reconstructionpartial relational specificationreverse_reconstruction
oracle_independenceoracle_independencepartial relational specificationoracle_independence
control_scopecontrol_scopepartial relational specificationcontrol_scope

Model text

descriptant

offline_dynamic_connectivity epoch memory

2026-10-30: choose exact bounded integer computation before implementation. 4096 timelines with six toggles, 60 post-toggle queries and one initial component query each. BFS rebuild scans all e edges per dequeued vertex, O(n+n*e), under tiny fixed n; cap fixtures allocate up to 2^18 timeline entries. No timing benchmark.

Retain the distinction between observation and internal representation: query ties preserve insertion identity; connectivity results preserve only partitions. The compiled faulty reduction/rollback controls establish sensitivity at named assertions. Original code follows the classic descriptions cited in module documentation; no copied solution.

No performance gain or approximate substitute claimed. These small files use file-level models, with no nested fragments. Source-bound partial syntax is generated twice identically; macro expansion and semantic AST remain absent. Allocation-failure behavior is not fault-injected.

model

offline_dynamic_connectivity tests.rs

Forward

Execute all 4^6 edge-toggle sequences over three vertices (including a self-loop), querying all nine ordered pairs and component count after each toggle. Rebuild active-edge BFS labels independently per query. Add lifecycle, empty-domain, rollback and cap witnesses.

Invariant

Fixture order and integer arithmetic deterministic; independent oracles do not invoke production helpers. Test outcome observes scheduled assertions only, not all possible inputs or allocation effects.

Cost

4096 timelines with six toggles, 60 post-toggle queries and one initial component query each. BFS rebuild scans all e edges per dequeued vertex, O(n+n*e), under tiny fixed n; cap fixtures allocate up to 2^18 timeline entries. No timing benchmark.

behavior_complement

Universe: implementations paired with normal/panic outcomes on the scheduled timelines. Normal completion is excluded when any connectivity/component answer disagrees with the independent active-edge BFS or literal rollback/lifecycle/cap assertions. Unsampled histories remain unconstrained.

reverse_reconstruction

Normal completion retains all implementations agreeing on the finite observations, including different algorithms and faults outside these fixtures. A failing named assertion yields a concrete witness, not a unique faulty source reconstruction. Finite success does not recover implementation identity.

oracle_independence

Execute all 4^6 edge-toggle sequences over three vertices (including a self-loop), querying all nine ordered pairs and component count after each toggle. Rebuild active-edge BFS labels independently per query. Add lifecycle, empty-domain, rollback and cap witnesses.

control_scope

One compiled production mutation is required to fail a named assertion. Exact saved bytes are restored before repeated positive runs. This witnesses sensitivity to that fault only; no exhaustive fault detection follows.

evidence

Evidence, 2026-10-30

Source SHA-256: c7f0e9526f087da03de94a426998d0db70f6d8db2b84a4e217647c2fea413380. Three tests for this algorithm pass twice debug and twice release with identical normalized names/results. Strict all-target Clippy and narrow rustfmt pass. One production mutant per algorithm compiles and fails a named assertion, then exact source bytes are restored.

4096 timelines with six toggles, 60 post-toggle queries and one initial component query each. BFS rebuild scans all e edges per dequeued vertex, O(n+n*e), under tiny fixed n; cap fixtures allocate up to 2^18 timeline entries. No timing benchmark.

Li Chao mutant changes query min reduction to max and fails exhaustive_envelopes. Connectivity mutant suppresses rollback and fails rollback_and_lifecycle. Six tests and two production controls total across the two algorithms. Finite evidence is not general correctness proof. No live parser/teacher/GPU, full-course or performance evidence.

External raw log hashes:

Structural receipts: four file sidecars, eighteen typed views (five per production file, four per tests file), zero fragments, four source-bound partial syntax projections. Each syntax artifact and groupant report generated twice identically. Temporary scaffold includes the base registry unchanged; no shared registry edits committed. Initial own-only scaffold was rejected for excluding existing ownership declarations, then corrected by including base nodes.

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