A Formalization and Proof of the Extended Church-Turing Thesis -Extended Abstract-

TL;DR

This paper formally proves the Extended Church-Turing Thesis by demonstrating that any effective algorithm can be efficiently simulated by a Turing machine through abstract state machines and minimal term graphs.

Contribution

It provides a formal proof of the Extended Church-Turing Thesis using a novel simulation approach involving abstract state machines and minimal term graphs.

Findings

Effective algorithms can be efficiently simulated by Turing machines.

The simulation uses abstract state machines and minimal term graphs.

The proof solidifies the theoretical foundation of the Extended Church-Turing Thesis.

Abstract

We prove the Extended Church-Turing Thesis: Every effective algorithm can be efficiently simulated by a Turing machine. This is accomplished by emulating an effective algorithm via an abstract state machine, and simulating such an abstract state machine by a random access machine, representing data as a minimal term graph.