# LLM-FSM: Scaling Large Language Models for Finite-State Reasoning in RTL Code Generation

arXiv: https://arxiv.org/abs/2602.07032 · HTML: https://mlsanity.com/paper/2602.07032/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 0 of its 52 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Placed in

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

## Built on by (most cited first, 2 of 2)

- [Exploring the Agentic Frontier of Verilog Code Generation](https://mlsanity.com/paper/2603.19347/) (2026)
- [BEHAVE: Functional Behavior Modeling Enables Self-Improving Agents for Hardware Design and Verification](https://mlsanity.com/paper/2609.34785/) (2026)

## Abstract (arXiv)

Finite-state reasoning, the ability to understand and implement state-dependent behavior, is central to hardware design. In this paper, we present LLM-FSM, a benchmark that evaluates how well large language models (LLMs) can recover finite-state machine (FSM) behavior from natural-language specifications and translate it into correct register transfer-level (RTL) implementations. Unlike prior specification-to-RTL benchmarks that rely on manually constructed examples, LLM-FSM is built through a fully automated pipeline. LLM-FSM first constructs FSM with configurable state counts and constrained transition structures. It then prompts LLMs to express each FSM in a structured YAML format with an application context, and to further convert that YAML into a natural-language (NL) specification. From the same YAML, our pipeline synthesizes the reference RTL and testbench in a correct-by-construction manner. All 1,000 problems are verified using LLM-based and SAT-solver-based checks, with human review on a subset. Our experiments show that even the strongest LLMs exhibit sharply declining accuracy as FSM complexity increases. We further demonstrate that training-time scaling via supervised fine-tuning (SFT) generalizes effectively to out-of-distribution (OOD) tasks, while increasing test-time compute improves reasoning reliability. Finally, LLM-FSM remains extensible by allowing its FSM complexity to scale with future model capabilities.