Optimal Symbolic Controllers Determinization for BDD storage

TL;DR

This paper addresses the challenge of reducing the size of symbolic controllers stored as BDDs by proposing new determinization methods, including greedy algorithms and symbolic regression, which significantly decrease controller size.

Contribution

It introduces the first formal analysis of the NP-completeness of optimal controller determinization and proposes novel algorithms to improve BDD-based controller storage.

Findings

New algorithms can produce controllers up to 85% smaller.

Demonstrates the NP-completeness of optimal determinization.

Empirical comparison shows improvements over existing methods.

Abstract

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.