Elamur Groupantsalgorithm-two-way-matching
The groupant beside algorithms/src/two_way_matching/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
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 |
| ast | partial | syntax.json |
| benchmark | bounded measured evidence | benchmark-wave18 |
| cost | symbolic unmeasured | Cost |
| descriptant | present | descriptant |
| invariant | source derived | Invariant |
| tests | bounded executed | 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 |
preimages | reverse_reconstruction | partial source derived | preimages |
critical-cut | state_preimage | partial source derived | critical-cut |
periodic-memory | refinement_relation | partial source derived | periodic-memory |
empty-long | domain_partition | partial source derived | empty-long |
byte-renaming | metamorphic_relation | partial source derived | byte-renaming |
Model text
descriptant
algorithm-two-way-matching
Prospective model saved before implementation in $MOVA_DATA/runs/octopus-wave18-strings-2026-10-30/prospective.md.
Return the ascending set {i | text[i..i+m]=pattern}; for m=0 return all n+1 byte boundaries. Critical factorization plus periodic memory implements Crochemore-Perrin (JACM 38, 1991).
Both ordered maximal suffix scans choose a critical cut. Right-half mismatch advances past impossible starts; after a complete right match, the left half certifies the candidate. A periodic shift retains only the prefix guaranteed by the pattern period.
Observed 2026-10-30: Binary pairs: 511 texts through length 8 times 127 patterns through length 6 = 64,897 independent window comparisons. Long periodic and nonperiodic cases, overlaps, empty boundaries and every byte. Mutation adds one to returned offsets; exhaustive_offsets fails.
Partial Rust syntax projection excludes macro expansion and semantic resolution. Finite tests do not prove general correctness or linear cost. No executable approximation profile: outputs are discrete exact objects and no useful certified surrogate metric is proposed.
model
algorithm-two-way-matching
Forward
Return the ascending set {i | text[i..i+m]=pattern}; for m=0 return all n+1 byte boundaries. Critical factorization plus periodic memory implements Crochemore-Perrin (JACM 38, 1991).
Invariant
Both ordered maximal suffix scans choose a critical cut. Right-half mismatch advances past impossible starts; after a complete right match, the left half certifies the candidate. A periodic shift retains only the prefix guaranteed by the pattern period.
Cost
O(n+m+z) byte comparisons and output work; O(1) scratch excluding z offsets. Slice lengths fit isize, and shift/index sums are at most n+m, hence fit usize. Output allocation may panic/abort; no output budget.
nonbehavior
No false or omitted offsets are allowed. Matching does not decode Unicode, fold case, or remove overlapping occurrences.
Domain: finite byte inputs and stated successful-allocation/representability premises. Observation: public call or named internal state. Status: source-derived exact target relation with bounded evidence, not a general proof.
preimages
For fixed pattern and offsets, the fiber consists of texts with exactly those occurrences and no others. Empty offsets generally admit many texts; even one match does not recover bytes outside the matched intervals.
Domain: finite byte inputs and stated successful-allocation/representability premises. Observation: public call or named internal state. Status: source-derived exact target relation with bounded evidence, not a general proof.
critical-cut
A cut and period retain patterns whose maximal suffix in one of two opposing byte orders attains that cut with the recorded period. They do not uniquely recover a pattern.
Domain: finite byte inputs and stated successful-allocation/representability premises. Observation: public call or named internal state. Status: source-derived exact target relation with bounded evidence, not a general proof.
periodic-memory
If the critical prefix equals the prefix displaced by period, a successful right-half scan permits retaining m-period bytes after shifting. Memory is cleared on a right-half mismatch.
Domain: finite byte inputs and stated successful-allocation/representability premises. Observation: public call or named internal state. Status: source-derived exact target relation with bounded evidence, not a general proof.
empty-long
Empty pattern has n+1 matches, including the end boundary. A longer nonempty pattern has no matches; these cases bypass factorization.
Domain: finite byte inputs and stated successful-allocation/representability premises. Observation: public call or named internal state. Status: source-derived exact target relation with bounded evidence, not a general proof.
byte-renaming
Any bijection of byte values preserves occurrence offsets although it may change the critical factorization and intermediate shifts.
Domain: finite byte inputs and stated successful-allocation/representability premises. Observation: public call or named internal state. Status: source-derived exact target relation with bounded evidence, not a general proof.
CPU measurement epoch wave18
Against KMP, repeated-prefix mismatch is 4.29–4.31x faster and dense periodic matching is about 1.10x faster on these fixtures. Random single-match and mismatch cases are about 1.05–1.06x and 1.26–1.27x slower, respectively. The linear asymptotic model predicted no universal speed ordering. See benchmark-wave18.md. These measurements calibrate constants on fixed fixtures; they do not prove an asymptotic bound or justify automatic production substitution.
evidence
Evidence, 2026-10-30
Source SHA-256: 59243a65cbe79def72d53aa7e6a929fdb4bc53bab1b5736cde5217e6d481acef.
Three tests for this algorithm passed twice in debug and twice with rustc -O, serial execution and identical normalized identities. Compiled mutation failed the named assertion; source restored byte exactly and positive suite passed again. Two source-bound partial syntax projections were byte identical.
Binary pairs: 511 texts through length 8 times 127 patterns through length 6 = 64,897 independent window comparisons. Long periodic and nonperiodic cases, overlaps, empty boundaries and every byte. Mutation adds one to returned offsets; exhaustive_offsets fails.
Logs under $MOVA_DATA/runs/octopus-wave18-strings-2026-10-30:
- two_way_matching-debug-1.log: de33458663ba04f1a6bd8396f80554f5ff651da16e05609af4a5752f98b67558
- two_way_matching-debug-2.log: de33458663ba04f1a6bd8396f80554f5ff651da16e05609af4a5752f98b67558
- two_way_matching-release-1.log: 2d08e9e9e1dae2e45b32aac537d93883f2cc86d0af32511656d560749d4bc2f0
- two_way_matching-release-2.log: 2d08e9e9e1dae2e45b32aac537d93883f2cc86d0af32511656d560749d4bc2f0
- two_way_matching-mutant.log: 07f1789e82142e5f44d86d6d3e5cb1f551bbf9d7a77df93b285f28270b33f5dd
- two_way_matching-restored.log: de33458663ba04f1a6bd8396f80554f5ff651da16e05609af4a5752f98b67558
- cargo-two_way_matching-debug-1.log: 82a7bd56891aa322f06f4bb39815df7d42d6e5914151485cc5d3d10a9c1cb006
- cargo-two_way_matching-debug-2.log: f0ea76ed5c031b20fb37025370d152cabc7dc2c44c4bd41c26ef664aadcaf8e0
- cargo-two_way_matching-release-1.log: 79594969a49e754fa88079c8660a09c9a34ce1ba68482b73cba904107e117af9
- cargo-two_way_matching-release-2.log: 3f2ed2a26c495cfade5eb554da26fed9479e3fea84ce5abc4a80f9eff492e714
Cargo focused suites also passed twice in debug and twice in release with matching normalized outcomes. Strict library Clippy passed. Temporary exports restored. Clippy log SHA-256: a5668d2636de8c7e7c3d3a1b6aea1da32174b64bee750b6b6cdfca8afc01a77b.
Partial Rust syntax projection excludes macro expansion and semantic resolution. Finite tests do not prove general correctness or linear cost. No executable approximation profile: outputs are discrete exact objects and no useful certified surrogate metric is proposed.
benchmark-wave18
Bounded CPU cost observation — 2026-10-30
Against KMP, repeated-prefix mismatch is 4.29–4.31x faster and dense periodic matching is about 1.10x faster on these fixtures. Random single-match and mismatch cases are about 1.05–1.06x and 1.26–1.27x slower, respectively. The linear asymptotic model predicted no universal speed ordering.
Source SHA-256 59243a65cbe79def72d53aa7e6a929fdb4bc53bab1b5736cde5217e6d481acef. Harness SHA-256 20b57c991f61192b2b05e085edf8303d56e43290fe10b7e1dfd36f10ffc9cccf. See full fixtures, timings, limitations and prospective model. Two executions retain exact outputs/checksums and all seven samples per method. This is an exact-API CPU comparison, not a Rust approximation profile or Mova training claim.
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