FAOPs: Normal Forms and an Algebra for AI Agent Workflows

Ali Mohammadi Shanghooshabad

Home/Archive/arXiv

arXiv · 2610.22061

FAOPs: Normal Forms and an Algebra for AI Agent Workflows

Ali Mohammadi Shanghooshabad

View original source ↗Read source document ↗Export metadata ↓

Abstract

Organizations increasingly encode operational procedures as multi-step agent skills, here called Agent Operating Procedures (AOPs), that must be traceable, auditable, reproducible, access-controlled, and bounded in time and cost, requirements that regulated sectors make mandatory. Yet AOPs are typically kept as coarse-grained files, in which steps bundle actions, copied procedures drift apart, any step may reach any tool, and refactoring goes unchecked. We present Functional Agent Operating Procedures (FAOP), a formal theory that brings database-grade discipline to AI agent workflows. FAOP recasts each workflow as a typed function over scoped state and subjects an entire library to four progressive normal forms: Decomposed (FNF-1) splits a workflow into atomic steps, Typed (FNF-2) makes its data flow explicit and type-checked, Factored (FNF-3) gives each shared procedure a single canonical definition so a change propagates instead of drifting, and Scoped (FNF-4) confines every step to least-privilege tool access. Once normalized, every atomic step is a separate entity with a declared contract and can be type-checked, scope-confined, bounded, tested, traced, and audited on its own. A FAOP algebra of provably sound equalities turns refactoring and parallelization into compiler rewrites; orthogonal extensions add verified termination (+V), optimization (+O), and time and cost bounds (+B); and an architectural-level classifier (0-3) determines whether a workflow needs AI at all. Together, these make integrity, isolation, typing, termination, cost, and optimization compile-time concerns across the whole library, not runtime hopes. We implement the theory in SkillBase, an AOP management system (what PostgreSQL is to data, SkillBase is to AOPs), together with a separate executor that enforces these guarantees at run time. A worked financial workflow illustrates the approach end to end.

Explore related subjects

cs.AI cs.DB cs.PL

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ali Mohammadi Shanghooshabad. 2026-10-15. FAOPs: Normal Forms and an Algebra for AI Agent Workflows. https://arxiv.org/abs/2610.22061

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Atomic Proximal Policy Optimization for Electric Robo-Taxi Dispatch and Charger Allocation

Pioneering companies such as Waymo have deployed electric robo-taxi services in several U.S. cities. Operating such fleets requires coordinating ride matching, vehicle repositioning, and battery charging in a stochastic environment while accounting for limited charging infrastructure. Understanding both how to design efficient, scalable control algorithms for large fleets and how charger deployment shapes system performance is therefore critical for robo-taxi operators. We model the operations of an electric robo-taxi system as a discrete-time Markov decision process with a long-run average reward objective. To efficiently evaluate system performance under different configurations, we develop a scalable deep reinforcement learning algorithm, Atomic Proximal Policy Optimization (Atomic-PPO), which reduces the action space using atomic action decomposition. The resulting training procedure requires only modest computational resources, making it practical to evaluate a large number of system configurations. We calibrate a simulation environment using real-world NYC for-hire vehicle trip records and benchmark Atomic-PPO against heuristic policies and a fluid-based reward upper bound. The results show that Atomic-PPO produces near-optimal fleet dispatching policies and serves as a reliable tool for system evaluation. We conduct extensive numerical experiments to evaluate how charging infrastructure and fleet size affect system performance. Our findings highlight the importance of ridership-based charger placement, balanced investments in charger quantity and charging speed, and joint planning of charging infrastructure and fleet size.

cs.AI↗

arXiv2026

Generalising from Self-Produced Data: Model Training Beyond Human Constraints

Current large language models (LLMs) are constrained by human-derived training data and limited by a single level of abstraction that impedes definitive truth judgments. This paper introduces a novel framework in which AI models autonomously generate and validate new knowledge through direct interaction with their environment. Central to this approach is an unbounded, ungamable numeric reward - such as annexed disk space or follower count - that guides learning without requiring human benchmarks. AI agents iteratively generate strategies and executable code to maximize this metric, with successful outcomes forming the basis for self-retraining and incremental generalisation. To mitigate model collapse and the warm start problem, the framework emphasizes empirical validation over textual similarity and supports fine-tuning via GRPO. The system architecture employs modular agents for environment analysis, strategy generation, and code synthesis, enabling scalable experimentation. This work outlines a pathway toward self-improving AI systems capable of advancing beyond human-imposed constraints toward autonomous general intelligence.

cs.AI↗

arXiv2026

Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis

Data synthesis for training large reasoning models offers a scalable alternative to limited, human-curated datasets, enabling the creation of high-quality data. However, existing approaches face several challenges: (i) indiscriminate generation that ignores the solver's ability and yields low-value problems, or reliance on complex data pipelines to balance problem difficulty; and (ii) a lack of reasoning in problem generation, leading to shallow problem variants. In this paper, we develop a problem generator that reasons explicitly to plan problem directions before synthesis and adapts difficulty to the solver's ability. We recover problem-design CoT from human-authored multi-part questions, using later subquestions as targets to infer the design rationale. These traces initialize the generator, which is then optimized with a seed-conditioned reward based on solver answer consistency. The reward guides difficulty adjustment relative to each seed while favoring problems near the solver's competence boundary. Across 10 mathematical and general reasoning benchmarks, our method outperforms seed-only training by 2.69 and 3.39 percentage points after one and three rounds, respectively. The framework also extends to vision-language models. Our code is publicly available at https://github.com/WalkerWorldPeace/Reasoning-Synthesis.

cs.AI↗