Computational Complexity of Interactive Behaviors

TL;DR

This paper extends computational complexity theory to fully general interactive behaviors using concurrency models, linking classical complexity classes with interactive process behaviors.

Contribution

It introduces a new theoretical framework for analyzing the intrinsic difficulty of interactive behaviors using concurrency theory tools.

Findings

Behavioral complexity aligns with classical classes in restricted cases

Uses labelled transition systems and asynchronous extensions for modeling

Provides a consistent extension of classical complexity theory to interaction

Abstract

The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing the intrinsic difficulty of fully general interactive behaviors. To this extent, we use standard tools from concurrency theory, including labelled transition systems (formalizing behaviors) and their asynchronous extension (providing causality information). Behaviors are implemented by means of a multiprocessor machine executing CCS-like processes. The resulting theory is shown to be consistent with the classical definitions: when we restrict to functional behaviors (i.e., question/answer patterns), we recover several standard computational complexity classes.