# A Correctness Result for Synthesizing Plans With Loops in Stochastic Domains

## TL;DR

This paper presents new theoretical results ensuring correctness when synthesizing finite-state controllers with loops in stochastic domains, addressing termination and goal-reaching guarantees.

## Contribution

It introduces a generic technique for synthesizing FSCs in stochastic environments with formal guarantees on termination and goal satisfaction.

## Key findings

- Provides a formal correctness framework for FSCs with loops in stochastic settings
- Enables highly granular specifications for termination and goal conditions
- Advances understanding of synthesis algorithms in probabilistic environments

## Abstract

Finite-state controllers (FSCs), such as plans with loops, are powerful and compact representations of action selection widely used in robotics, video games and logistics. There has been steady progress on synthesizing FSCs in deterministic environments, but the algorithmic machinery needed for lifting such techniques to stochastic environments is not yet fully understood. While the derivation of FSCs has received some attention in the context of discounted expected reward measures, they are often solved approximately and/or without correctness guarantees. In essence, that makes it difficult to analyze fundamental concerns such as: do all paths terminate, and do the majority of paths reach a goal state? In this paper, we present new theoretical results on a generic technique for synthesizing FSCs in stochastic environments, allowing for highly granular specifications on termination and goal satisfaction.