# GenOS: Compositional Certificates for Semantic Robustness in AI Code Generation

arXiv: https://arxiv.org/abs/2608.03588 · HTML: https://mlsanity.com/paper/2608.03588/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Software engineering coding agents, one of 16 directions in LLM agents and tool use.
- Builds on 8 of its 17 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Placed in

- LLM agents and tool use / [Software engineering coding agents](https://mlsanity.com/agents/software-engineering-coding-agents/)

## Builds on (most cited first, 8 of 8)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Prompting Is Programming: A Query Language for Large Language Models](https://mlsanity.com/paper/2212.06094/) (2022)
- [Jigsaw: Large Language Models meet Program Synthesis](https://mlsanity.com/paper/2112.02969/) (2021)
- [Clover: Closed-Loop Verifiable Code Generation](https://mlsanity.com/paper/2310.17807/) (2023)
- [Enchanting Program Specification Synthesis by Large Language Models using Static Analysis and Program Verification](https://mlsanity.com/paper/2404.00762/) (2024)
- [VeCoGen: Automating Generation of Formally Verified C Code with Large Language Models](https://mlsanity.com/paper/2411.19275/) (2024)

## Abstract (arXiv)

AI coding agents are stochastic workflows: prompts are interpreted, artifacts are sampled, validators produce observations, and orchestrators commit or repair. Small prompt or specification changes can therefore alter program-behavior distributions even when the texts appear synonymous. Existing systems evaluate correctness, but lack a compositional criterion for safely replacing a prompt, contract, generator, or program inside a complete agentic workflow. We introduce GenOS, a probabilistic operational semantics for this replacement problem. Each layer is modeled as a Markov kernel, and each interface carries an observer-relative equivalence. We prove that equivalence-compatible kernels descend to quotient classes and that quotienting commutes with distributional extension and sequential composition. Hence, equivalent prompts induce equal probabilities for all downstream equivalence-closed events, including verified commit. We also establish workflow bisimulation, guarded-commit safety under sound validation, total-variation non-expansiveness, and an additive robustness bound that attributes approximation error to individual pipeline layers. An executable insertion-sort audit instantiates the theory with natural-language paraphrases, a formal contract, six programs, two observers, and exhaustive execution on 121 inputs. Equivalent prompts yield identical code-class and commit distributions; a prompt assigning 5% probability to an in-place contract is distinguished by a mutation observer, while downstream distances remain within the predicted bound. Across 20,000 randomized finite-kernel trials, no exact or approximate law is violated. GenOS is model-parametric: compatibility is a measurable property to test, not an assumption about language-model behavior.