# Optimal Symbolic Controllers Determinization for BDD storage

arXiv: https://arxiv.org/abs/1803.07369 · HTML: https://mlsanity.com/paper/1803.07369/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2018.

## Built on by (most cited first, 4 of 4)

- [dtControl 2.0: Explainable Strategy Representation via Decision Tree Learning Steered by Experts](https://mlsanity.com/paper/2101.07202/) (2021)
- [Algebraically Explainable Controllers: Decision Trees and Support Vector Machines Join Forces](https://mlsanity.com/paper/2208.12804/) (2022)
- [Neural Abstraction-Based Controller Synthesis and Deployment](https://mlsanity.com/paper/2307.03783/) (2023)
- [Explaining Control Policies through Predicate Decision Diagrams](https://mlsanity.com/paper/2503.06420/) (2025)

## Abstract (arXiv)

Controller synthesis techniques based on symbolic abstractions appeal by producing correct-by-design controllers, under intricate behavioural constraints. Yet, being relations between abstract states and inputs, such controllers are immense in size, which makes them futile for em- bedded platforms. Control-synthesis tools such as PESSOA, SCOTS, and CoSyMA tackle the problem by storing controllers as binary decision di- agrams (BDDs). However, due to redundantly keeping multiple inputs per-state, the resulting controllers are still too large. In this work, we first show that choosing an optimal controller determinization is an NP- complete problem. Further, we consider the previously known controller determinization technique and discuss its weaknesses. We suggest several new approaches to the problem, based on greedy algorithms, symbolic regression, and (muli-terminal) BDDs. Finally, we empirically compare the techniques and show that some of the new algorithms can produce up to 85% smaller controllers than those obtained with the previous technique.