Creating Teams of Simple Agents for Specified Tasks: A Computational Complexity Perspective

TL;DR

This paper analyzes the computational complexity of designing and verifying teams of simple agents for specific tasks, showing that these problems are generally intractable, thus highlighting the need for restrictions or heuristics.

Contribution

It provides a formal complexity analysis demonstrating the intractability of automated team verification and design for simple agents communicating indirectly.

Findings

Automated team verification is computationally intractable in general.

Automated team design is computationally intractable in general.

Tractability may require restrictions on teams, agents, environments, or tasks.

Abstract

Teams of interacting and co-operating agents have been proposed as an efficient and robust alternative to monolithic centralized control for carrying out specified tasks in a variety of applications. A number of different team and agent architectures have been investigated, e.g., teams based on single vs multiple behaviorally-distinct types of agents (homogeneous vs heterogeneous teams), simple vs complex agents, direct vs indirect agent-to-agent communication. A consensus is emerging that (1) heterogeneous teams composed of simple agents that communicate indirectly are preferable and (2) automated methods for verifying and designing such teams are necessary. In this paper, we use computational complexity analysis to assess viable algorithmic options for such automated methods for various types of teams. Building on recent complexity analyses addressing related questions in swarm robotics, we prove that automated team verification and design are by large both exact and approximate polynomial-time intractable in general for the most basic types of homogeneous and heterogeneous teams consisting of simple agents that communicate indirectly. Our results suggest that tractability for these problems must be sought relative to additional restrictions on teams, agents, operating environments, and tasks.