Topological Interpretation of Interactive Computation

TL;DR

This paper introduces a topological framework for modeling interactive computation, proposing a topological Turing machine as a universal model that captures the essence of sequential and concurrent interactions.

Contribution

It presents a novel topological setting to formalize environments and defines a topological Turing machine as a new universal model for interactive and potentially concurrent computation.

Findings

Topological Turing machine as a universal model

Formalization of environment using topology

Potential application to concurrent computation

Abstract

It is a great pleasure to write this tribute in honor of Scott A. Smolka on his 65th birthday. We revisit Goldin, Smolka hypothesis that persistent Turing machine (PTM) can capture the intuitive notion of sequential interaction computation. We propose a topological setting to model the abstract concept of environment. We use it to define a notion of a topological Turing machine (TTM) as a universal model for interactive computation and possible model for concurrent computation.