2024/12/01 by Ali Asadi, Asadi, Ali, Krishnendu Chatterjee +5
Computer Science · Engineering · #Computational Complexity (cs.CC) #FOS: Computer and information sciences #Low-power high-performance VLSI design #Parallel Computing and Optimization Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2412.00941
openalex publication_date 2024/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A standard model that arises in several applications in sequential decision making is partially observable Markov decision processes (POMDPs) where a decision-making agent interacts with an uncertain environment. A basic objective in such POMDPs is the reachability objective, where given a target set of states, the goal is to eventually arrive at one of them. The limit-sure problem asks whether reachability can be ensured with probability arbitrarily close to 1. In general, the limit-sure reachability problem for POMDPs is undecidable. However, in many practical cases the most relevant question is the existence of policies with a small amount of memory. In this work, we study the limit-sure reachability problem for POMDPs with a fixed amount of memory. We establish that the computational complexity of the problem is NP-complete.