# A Mathematical Characterization of Minimally Sufficient Robot Brains

arXiv: https://arxiv.org/abs/2308.09041 · HTML: https://mlsanity.com/paper/2308.09041/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 66 references that are in the map.
- First posted on arXiv 17 Aug 2023.

## Builds on (most cited first, 11 of 11)

- [Online Planning Algorithms for POMDPs](https://mlsanity.com/paper/1401.3436/) (2014)
- [Funnel Libraries for Real-Time Robust Feedback Motion Planning](https://mlsanity.com/paper/1601.04037/) (2016)
- [Latent Imagination Facilitates Zero-Shot Transfer in Autonomous Racing](https://mlsanity.com/paper/2103.04909/) (2021)
- [Incremental Pruning: A Simple, Fast, Exact Method for Partially Observable Markov Decision Processes](https://mlsanity.com/paper/1302.1525/) (2013)
- [Hilbert Space Embeddings of Predictive State Representations](https://mlsanity.com/paper/1309.6819/) (2013)
- [Co-Design of Autonomous Systems: From Hardware Selection to Control Synthesis](https://mlsanity.com/paper/2011.10758/) (2020)
- [Toward a language-theoretic foundation for planning and filtering](https://mlsanity.com/paper/1807.08856/) (2018)
- [Abstractions for computing all robotic sensors that suffice to solve a planning problem](https://mlsanity.com/paper/2005.10994/) (2020)
- [An Enactivist-Inspired Mathematical Model of Cognition](https://mlsanity.com/paper/2206.06096/) (2022)
- [Lattices of sensors reconsidered when less information is preferred](https://mlsanity.com/paper/2106.00805/) (2021)
- [The Limits of Learning and Planning: Minimal Sufficient Information Transition Systems](https://mlsanity.com/paper/2212.00523/) (2022)

## Built on by (most cited first, 5 of 5)

- [Semantic Communication meets System 2 ML: How Abstraction, Compositionality and Emergent Languages Shape Intelligence](https://mlsanity.com/paper/2505.20964/) (2025)
- [Toward Learning POMDPs Beyond Full-Rank Actions and State Observability](https://mlsanity.com/paper/2601.18930/) (2026)
- [Logic-Driven Semantic Communication for Resilient Multi-Agent Systems](https://mlsanity.com/paper/2601.06733/) (2026)
- [Active Reward Machine Inference From Raw State Trajectories](https://mlsanity.com/paper/2604.07480/) (2026)
- [RingNav: Task-Shaped Circular Memory for Visual Heading](https://mlsanity.com/paper/2610.19044/) (2026)

## Abstract (arXiv)

This paper addresses the lower limits of encoding and processing the information acquired through interactions between an internal system (robot algorithms or software) and an external system (robot body and its environment) in terms of action and observation histories. Both are modeled as transition systems. We want to know the weakest internal system that is sufficient for achieving passive (filtering) and active (planning) tasks. We introduce the notion of an information transition system for the internal system which is a transition system over a space of information states that reflect a robot's or other observer's perspective based on limited sensing, memory, computation, and actuation. An information transition system is viewed as a filter and a policy or plan is viewed as a function that labels the states of this information transition system. Regardless of whether internal systems are obtained by learning algorithms, planning algorithms, or human insight, we want to know the limits of feasibility for given robot hardware and tasks. We establish, in a general setting, that minimal information transition systems exist up to reasonable equivalence assumptions, and are unique under some general conditions. We then apply the theory to generate new insights into several problems, including optimal sensor fusion/filtering, solving basic planning tasks, and finding minimal representations for modeling a system given input-output relations.