📐algorithm-meet-in-middle-knapsack

The groupant beside algorithms/src/meet_in_middle_knapsack/mod.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

Components

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.

Model text

descriptant

meet_in_middle_knapsack mod.rs

Original std-only implementation and independent fixtures. Horowitz and Sahni (1974), Computing partitions with applications to the knapsack problem.

Prospective model saved before changes in $MOVA_DATA/runs/octopus-wave20-dp-2026-10-30/prospective.md. Current epoch 2026-10-30: exact optimization with explicit bounded-resource outcomes. Finite oracle agreement does not establish the caller's monotonicity premises. No timing or whole-Mova speed claim.

approximant

Forward model

Split items in halves; enumerate feasible (weight,value) subsets, right sorted by weight then value. Prefix maxima answer max_{right.weight<=capacity-left.weight} right.value. Combine each feasible left state exactly once.

Cost

O(n*2^ceil(n/2)) time, O(2^ceil(n/2)) states. max_states bounds sum of full half powers before allocations, even if pruning would reduce counts. Checked dimensions, u128 candidate sums; weights add only after capacity subtraction guard.

Invariants and limits

Owned input slices remain unchanged. Deterministic ties and traversal; callback panics propagate and purity/monotonicity remain caller obligations. No allocator-refusal injection, no semantic AST proof, no universal finite-test proof. Checked arithmetic reports errors rather than wrapping.

Executable approximant gap

No executable surrogate is attached: categorical reachability/argmin has no justified relaxed metric here. Objective-only surrogate speed/error has not been measured. Existing knapsack surrogate is not automatically transferable. No 1/2/5/10% profile or approximate substitution is claimed.

models

behavior_complement

For one Item(weight=2,value=7) and capacity 1, any positive objective is excluded. A returned objective excludes all larger feasible subset values.

reverse_reconstruction

Objective 0 at capacity 0 admits [] and [(1,7)]. Positive objective 7 at capacity 2 admits [(2,7)] or [(1,3),(1,4)]. No subset identity can be uniquely recovered.

permutation

Reordering items changes the half split and enumeration but preserves optimum when both resource checks succeed.

zero_extension

Appending (0,v) raises optimum by exactly v, provided state budget and checked sums permit.

capacity_monotonicity

Increasing capacity cannot decrease successful objective; the resource count is capacity-independent.

dominance_envelope

At each sorted right index, envelope value equals the maximum raw value in that prefix. Discarding a lower value at equal or greater weight preserves every feasible left query.

tests

Checks

cargo test -p mova-algorithms meet_in_middle_knapsack::tests

Independent small oracle and resource boundary fixtures live in ../tests.rs. Repeated debug/release and compiled mutation receipts: $MOVA_DATA/runs/octopus-wave20-dp-2026-10-30.

combiner

Composition

Raw mod.rs syntax and mathematical recurrence are separate evidence. The partial syntax projection binds the exact source bytes but does not certify the recurrence. Oracle tests compare observable outputs; typed relations constrain lawful transformations and compatible preimages. For meet_in_middle_knapsack, resource caps and checked failures remain separate from mathematical objective equivalence. Prospective expectations remain unchanged; finite validation cannot turn monotonicity assumptions into runtime validation.

validation

Validation — 2026-10-30

Ten new native tests cover five exact kernels. Full mova-algorithms library: 557 tests pass in two debug and two release executions; sorted native test outcomes agree byte-for-byte across all four. Strict all-target Clippy and focused rustfmt pass. External receipts: $MOVA_DATA/runs/octopus-wave20-dp-2026-10-30/{debug1,debug2,release1,release2,clippy}.log.

Compiled production controls: zero initial subset bit, forced zero MITM objective, right-tie SMAWK reduction, forced zero layered-DP objective and forced zero BST objective all fail named equality assertions. Byte restoration followed by full positive library rerun passes. A separate SMAWK interpolation tie mutation fails lawful_matrices after adding half-integer squared-distance centers; the restored focused test passes. Receipts: controls.log, mutant-*.log, restored.log, smawk-restored.log in the same external run directory. The original constant-matrix fixture alone did not distinguish interpolation ties; the stronger fixture closes that observed gap.

Every source/test file has two independently generated identical syntax projections and current source SHA. An isolated ten-leaf modelcheck groupants run reports valid=true, diagnostics=[], ten sidecars, zero missing source sidecars; the temporary collection parent has no sidecar and makes no composition claim. Root integration owns global registry and ancestor binding checks.

No timing speedup, machine-independent resource guarantee, allocation-failure injection, monotonicity validation, or end-to-end Mova improvement is inferred. Successful finite tests certify the listed observations only. No teacher, model, corpus or live database operations were used.

This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/algorithms/src/meet_in_middle_knapsack/mod.rs.groupant/