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

The groupant beside algorithms/src/viterbi/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 descriptive instance
- **source:** [`algorithms/src/viterbi/tests.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/viterbi/tests.rs)
- **source SHA-256:** `23671e35aee086da…`
- **repository folder:** [`algorithms/src/viterbi/tests.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/viterbi/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** | partial | [approximant](#approximant) |
| **ast** | partial | `syntax.json` |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [model](#model) |
| **tests** | existing checks referenced | [tests](#tests) |

## 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 |
|---|---|---|---|
| `behavior_complement` | behavior_complement | partial source derived model | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) |
| `independent_oracle` | independent_oracle | partial source derived model | [independent_oracle](#independent-oracle) |
| `boundary_partition` | boundary_partition | partial source derived model | [boundary_partition](#boundary-partition) |
| `compiled_mutation` | compiled_mutation | partial source derived model | [compiled_mutation](#compiled-mutation) |

## Model text


### descriptant

#### viterbi checks

Original std-only implementation and fixtures; source citations appear in module documentation.

Independent finite oracle and boundary tests for viterbi. Production: n1..64,T0..4096; initial and transition rows normalized within1e-10, entries finite in[0,1]; emissions time-major in[0,1]. Shape precedes probability then normalization. log score(t,j)=log emission(t,j)+max_i(score(t-1,i)+log transition(i,j)); store predecessor. Empty sequence returns empty path/log0; impossible returns None.

Epoch 2026-10-30: independent tiny-domain oracle, repeated debug/release and compiled production mutation. No timing or end-to-end Mova claims.

### model

#### Invariants and state

Independent finite oracle and boundary tests for viterbi. Production: n1..64,T0..4096; initial and transition rows normalized within1e-10, entries finite in[0,1]; emissions time-major in[0,1]. Shape precedes probability then normalization. log score(t,j)=log emission(t,j)+max_i(score(t-1,i)+log transition(i,j)); store predecessor. Empty sequence returns empty path/log0; impossible returns None.

All-pass excludes represented oracle mismatches and rejected boundary violations in these finite fixtures only. Production excluded-output relation: Any path with strictly lower represented max-plus score than the selected terminal score is excluded. None excludes positive-probability paths in the validated model. Structural or numeric errors exclude a success even for empty emissions.

O(T*n*n) arithmetic, O(T*n) storage, bounded standard allocation.

All allocations follow standard Rust process policy, not fallible allocation APIs. No callbacks or external effects. f64 roundoff and underflow remain explicit limitations.

### approximant

#### Forward and cost approximant

Independent finite oracle and boundary tests for viterbi. Production: n1..64,T0..4096; initial and transition rows normalized within1e-10, entries finite in[0,1]; emissions time-major in[0,1]. Shape precedes probability then normalization. log score(t,j)=log emission(t,j)+max_i(score(t-1,i)+log transition(i,j)); store predecessor. Empty sequence returns empty path/log0; impossible returns None.

O(T*n*n) arithmetic, O(T*n) storage, bounded standard allocation.

No executable cheaper surrogate or supported generic 1/2/5/10% profile is claimed. Residuals and floating estimates are not solution-error certificates.

### models

### behavior_complement

All-pass excludes represented oracle mismatches and rejected boundary violations in these finite fixtures only. Production excluded-output relation: Any path with strictly lower represented max-plus score than the selected terminal score is excluded. None excludes positive-probability paths in the validated model. Structural or numeric errors exclude a success even for empty emissions.

### reverse_reconstruction

All-pass observations admit implementations differing on unsampled inputs. This finite test fiber does not uniquely identify source or prove universality. Production fiber: A selected state path and log score admit infinitely many HMMs differing on unused edges, subject to the path remaining optimal. The path cannot recover initial probabilities or the full transition matrix.

### independent_oracle

Tiny path enumeration, analytical rank-one matrices or independent weighted moments reconstruct expectations without calling the production recurrence; scope is finite.

### boundary_partition

Shape, zero/empty, invalid finite values, ties or budget boundaries are explicitly asserted. Numeric tolerance is fixture-specific.

### compiled_mutation

A compiled changed production recurrence must fail the named oracle assertion. Restoration plus positive rerun checks that the gate can distinguish this wrong behavior.

### tests

#### Validation

Run cargo test -p mova-algorithms viterbi::tests. Evidence in $MOVA_DATA/runs/octopus-wave26-probability-2026-10-30: repeated profiles, mutation logs and restored positive runs. Three named tests per module. See receipt.json for evidence hashes. No allocator fault injection, timing or full-school measurement.

### prospective

#### Probability batch prospective math

Written before implementation. All code original, std-only. Bounded allocations use standard Vec; allocator failure follows Rust process policy, no callbacks or RNG.

Alias: Walker (1977), An efficient method for generating discrete random variables with general distributions; Vose (1991), A linear algorithm for generating random numbers with a given distribution. n 1..4096, finite nonnegative weights, positive maximum. Scale by maximum then total to avoid overflow. Small/large work lists conserve total scaled mass. Column uniform and coin uniform [0,1) produce the specified categorical distribution in real arithmetic; caller explicitly supplies coordinates. O(n) build/storage, O(1) draw. No probabilistic draw generation or numeric percentage guarantee.

HMM: Rabiner (1989), A tutorial on hidden Markov models and selected applications in speech recognition; Viterbi (1967), Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. n1..64, T0..4096; finite probabilities in [0,1], initial/transition rows sum to one within 1e-10. Emissions time-major likelihoods in [0,1], need not sum across states. Validate structure then numeric values before empty sequence. Empty log likelihood0/path empty. Viterbi log max-plus recurrence, predecessor ties lowest index and terminal ties lowest index (not global lexicographic). No positive path =>None. Forward/backward log-sum-exp, posterior proportional exp(alpha+beta-logZ); per-row normalization corrects rounding. O(Tn²) time/O(Tn) space. Tiny exhaustive state-sequence enumeration is independent oracle. Log scales avoid direct-product underflow; no general floating error bound.

Sinkhorn: Sinkhorn and Knopp (1967), Concerning nonnegative matrices and doubly stochastic matrices. Positive matrix entries and marginals restricted [1e-100,1e100], dims1..64, equal marginal totals within tolerance1e-12 relative. Alternate row and column multiplication to target marginals; residual max absolute marginal discrepancy. Budget0..10000, finite tolerance>0. Stop on residual<=tolerance or budget; overflow/underflow to zero explicit arithmetic error. O(iterations*r*c) time/O(rc) space. Residual is feasibility evidence, not solution distance/optimality guarantee. Scale-invariant input fibers and budget status explicit.

Weighted covariance: West (1979), Updating mean and variance estimates: an improved method; Chan, Golub, LeVeque (1983), Algorithms for computing the sample variance. dimension1..64; finite coordinates |x|<=1e100, weights[0,1e100]. Population covariance M2/W, not unbiased sample covariance. Zero weight validates coordinates then does nothing. Merge dimensions must match, empty neutral. Merge W=A+B; delta=muB-muA; mu=muA+delta*B/W; M2=M2A+M2B+delta outer delta*A*(B/W). Atomic error updates, finite intermediates required. O(d²) push/merge/storage. Independent batch weighted centered moments oracle, partition merge equivalence within tolerance. No order-bitwise identity or universal covariance error certificate.