---
title: "algorithm-dominators — Mova code model"
description: "Mova code model of algorithms/src/dominators/mod.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/dominators/mod.rs.groupant/"
---
Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants**

This page as HTML: <https://groupants.elamur.ai/free/en/mova/algorithms/src/dominators/mod.rs.groupant/>

# algorithm-dominators

The groupant beside algorithms/src/dominators/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

- **kind:** groupant
- **status:** partial source derived instance
- **source:** [`algorithms/src/dominators/mod.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/dominators/mod.rs)
- **source SHA-256:** `86ec8acb6ff360b7…`
- **repository folder:** [`algorithms/src/dominators/mod.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/dominators/mod.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) |
| `compatible_inputs` | reverse_reconstruction | partial source derived | [compatible_inputs](#compatible-inputs) |
| `deletion_certificate` | path_obstruction | partial source derived | [deletion_certificate](#deletion-certificate) |
| `row_permutation` | representation_invariance | partial source derived | [row_permutation](#row-permutation) |
| `edge_extension` | antitone_extension | partial source derived | [edge_extension](#edge-extension) |
| `self_and_start` | endpoint_law | partial source derived | [self_and_start](#self-and-start) |

## Model text


Migration: consolidated into model.md, 2026-11-04, operator decision; fresh hash-bound references to the former files were rebound to the sections below.

### descriptant

#### dominators mod

Original std-only Rust. Prospective model is retained beside implementation. Source citations identify algorithm provenance; no copied implementation. Exact bounded graph semantics are useful independently of any unmeasured optimization. Finite oracle checks and mutant discrimination improve confidence; groupant count alone proves no improvement.

### model

## dominators mod model

### Forward

Directed graph n<=256,m<=65536 with duplicate arcs allowed. Valid start; unreachable vertices output empty. Initialize each reachable non-start dominator set to reachable universe, intersect predecessor sets plus vertex until fixed point; start singleton. O(V^2(V+E)) time conservative, O(V^2+E) memory. Iterative, no recursion. Aho, Sethi, Ullman Compilers (1986). No Lengauer-Tarjan complexity claim.

### Invariant

Unreachable rows remain empty; start remains singleton. Reachable rows shrink monotonically, remain supersets of true dominators, and satisfy predecessor intersection at termination.

### Cost

Directed graph n<=256,m<=65536 with duplicate arcs allowed. Valid start; unreachable vertices output empty. Initialize each reachable non-start dominator set to reachable universe, intersect predecessor sets plus vertex until fixed point; start singleton. O(V^2(V+E)) time conservative, O(V^2+E) memory. Iterative, no recursion. Aho, Sethi, Ullman Compilers (1986). No Lengauer-Tarjan complexity claim.

### nonbehavior

Type: behavior_complement. Let R be the deterministic relation specified by Forward including validation precedence and tie rules, X the declared input type and Y its Result type. Behavior complement is (X times Y) minus R. Specifically outputs violating Unreachable rows remain empty; start remains singleton. Reachable rows shrink monotonically, remain supersets of true dominators, and satisfy predecessor intersection at termination. are excluded; a valid-input Err or a wrong successful witness is excluded. Resource, cycle and structural rejections are determined before algorithmic output.

### compatible_inputs

Type: reverse_reconstruction. Given D, antecedents are graphs whose start-to-v paths all contain exactly D[v] as universal vertices; unreachable v have empty rows. A chain and the chain plus self-loops have identical D, so original edges cannot be recovered.

### deletion_certificate

Type: path_obstruction. For reachable v, d belongs to D[v] iff removing d makes v unreachable from start, counting removed start as reaching nothing.

### row_permutation

Type: representation_invariance. Permuting rows internally or duplicating edges preserves all dominator sets.

### edge_extension

Type: antitone_extension. Adding edges can only remove dominators from vertices already reachable; new reachability must be treated separately.

### self_and_start

Type: endpoint_law. For every reachable v, both start and v belong to D[v]; D[start]={start}. A disconnected component contributes no dominators regardless of its cycles.

### Limits

Partial syntax omits macro expansion and type resolution. No executable approximate profile: categorical graph semantics and feasibility have no justified percentage relaxation here. Integer operations are bounded by caps; flow uses checked i128/u64 arithmetic, with Overflow defensive under current caps. No callbacks. Allocator failure is outside typed status.

### evidence

#### Evidence — 2026-10-30

Eleven tests across five algorithms, including independent exhaustive small-domain characterization. This file belongs to dominators. Two debug and two optimized runs matched normalized statuses. Strict clippy-driver --test -D warnings passed. A compiled production mutant failed a named assertion; exact bytes restored and positive rerun passed. Raw receipts: $MOVA_DATA/runs/octopus-wave25-graphs-2026-10-30/dominators-*.txt. No timing or whole-system improvement claim. Source SHA-256: 86ec8acb6ff360b7264aed23b0c9925626f994bcca5515f63ff5703035c4e733.

### prospective

#### Prospective model — 2026-10-30

Directed graph n<=256,m<=65536 with duplicate arcs allowed. Valid start; unreachable vertices output empty. Initialize each reachable non-start dominator set to reachable universe, intersect predecessor sets plus vertex until fixed point; start singleton. O(V^2(V+E)) time conservative, O(V^2+E) memory. Iterative, no recursion. Aho, Sethi, Ullman Compilers (1986). No Lengauer-Tarjan complexity claim.
Allocation failure is outside typed errors. Resource caps precede vertex/edge validation. No callbacks. Exact categorical output has no justified percentage surrogate; executable approximation profiles unsupported.