# Rethinking Complexity Metrics for LLM-Integrated Applications: Beyond Source Code

arXiv: https://arxiv.org/abs/2607.01903 · HTML: https://mlsanity.com/paper/2607.01903/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 9 of 9)

- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [Large Language Model based Multi-Agents: A Survey of Progress and Challenges](https://mlsanity.com/paper/2402.01680/) (2024)
- [Inside the Scaffold: A Source-Code Taxonomy of Coding Agent Architectures](https://mlsanity.com/paper/2604.03515/) (2026)
- [A Taxonomy of Prompt Defects in LLM Systems](https://mlsanity.com/paper/2509.14404/) (2025)
- [HoarePrompt: Structural Reasoning About Program Correctness in Natural Language](https://mlsanity.com/paper/2503.19599/) (2025)
- [Unified Tool Integration for LLMs: A Protocol-Agnostic Approach to Function Calling](https://mlsanity.com/paper/2508.02979/) (2025)
- [Prompts as Software Engineering Artifacts: A Research Agenda and Preliminary Findings](https://mlsanity.com/paper/2509.17548/) (2025)
- [PromptDebt: A Comprehensive Study of Technical Debt Across LLM Projects](https://mlsanity.com/paper/2509.20497/) (2025)
- [AI-Generated Smells: An Analysis of Code and Architecture in LLM and Agent-Driven Development](https://mlsanity.com/paper/2605.02741/) (2026)

## Abstract (arXiv)

LLM-integrated applications blend natural language prompts with program code, and much of their runtime behavior originates in the prompt layer rather than in the code itself. Existing complexity metrics, however, operate solely at the code level and therefore overlook this behavioral logic entirely. We present HECATE, the first tool designed to assess complexity in both the prompt and code layers of such applications. Central to HECATE is Prompt-as-Specification, a Hoare-logic-inspired formalism that interprets every prompt as a specification of intended behavior. Grounded in 25 complexity dimensions identified across published taxonomies, the tool generates 52 candidate metrics. We assess each metric against 118 components collected from 18 open-source repositories, relying on maintenance activity derived from version history as an empirical proxy for complexity, and discard any metric that loses significance once code size is accounted for. Only ten metrics withstand this test. Seven belong to our newly introduced set; rather than measuring sheer volume, each tallies structurally distinct elements, such as LLM call sites, memory attributes, and prompt templates, an attribute we call structural breadth. Of the three surviving conventional metrics, RFC exhibits a similar breadth-oriented character, while Halstead N and V survive only as a residual effect of size; our top-performing metrics exceed all three. Crucially, the prompt-layer metrics retain significance even when the strongest code-level metric is added as a covariate, establishing prompt complexity as a dimension in its own right. A final validation on 20 components spanning six held-out repositories shows that the two best-performing metrics continue to predict maintenance effort, supporting their generalizability beyond the training set.