📐algorithm-divide-conquer-dp

The groupant beside algorithms/src/divide_conquer_dp/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

divide_conquer_dp mod.rs

Original std-only implementation and independent fixtures. Yao (1980), Efficient dynamic programming using quadrangle inequalities; monotone divide-and-conquer recurrence.

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

D[0,0]=0, other states unreachable; D[g,j]=min_{g-1<=k<j}(D[g-1,k]+cost(k,j)). Divide midpoint and restrict each child's candidate range by leftmost optimum. Caller guarantees monotone leftmost split in each row; pure deterministic cost callback; assumption is not checked.

Cost

O(layersnlog(n)) evaluations, O(n) storage. Budget checked before callback; all visited candidate sums checked (overflow fails even for a losing candidate). Impossible partitions handled before dimensions/allocation. g=0 yields 0 only for n=0.

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

Nonempty n with zero layers excludes any finite result. For squared interval length, n=8,g=3, result 21 is excluded; optimal lengths 2,3,3 cost 22.

reverse_reconstruction

A partition objective does not recover intervals or costs: for n=g=1 every callback with cost(0,1)=v maps to v regardless of other entries. For n=2,g=1 only cost(0,2) is observed.

constant_shift

Adding b to every interval cost raises the feasible optimum by layers*b, provided all evaluated arithmetic fits; split ordering remains unchanged.

positive_scale

Multiplication by positive integer preserves left argmins and scales result when all checked candidate sums fit.

lawful_cost_family

For nonnegative prefix sums P, cost(i,j)=(P[j]-P[i])^2 is Monge; its DP layers have monotone leftmost optimal splits. Exhaustive fixtures use this premise.

budget_prefix

At most max_evaluations callbacks occur; unreachable predecessor candidates incur no callback and no arithmetic.

tests

Checks

cargo test -p mova-algorithms divide_conquer_dp::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 divide_conquer_dp, 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/divide_conquer_dp/mod.rs.groupant/