Logical Characterization of Coherent Uninterpreted Programs
Bibliographic record
Abstract
An uninterpreted program (UP) is a program whose semantics is defined over the theory of uninterpreted functions.This is a common abstraction used in equivalence checking, compiler optimization, and program verification.While simple, the model is sufficiently powerful to encode counter automata, and, hence, undecidable.Recently, a class of UP programs, called coherent, has been proposed and shown to be decidable.We provide an alternative, logical characterization, of this result.Specifically, we show that every coherent program is bisimilar to a finite state system.Moreover, an inductive invariant of a coherent program is representable by a formula whose terms are of depth at most 1.We also show that the original proof, via automata, only applies to programs over unary uninterpreted functions.While this work is purely theoretical, it suggests a novel abstraction that is complete for coherent programs but can be soundly used on arbitrary uninterpreted (and partially interpreted) programs.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".