Zeno Squeezing of Cellular Automata

TL;DR

This paper introduces and surveys self-similar cellular automata and Petri nets, models capable of hypercomputations, including solving the halting problem, and discusses their properties and indeterminism.

Contribution

It presents new models of self-similar automata and Petri nets, expanding the understanding of hypercomputational systems and their indeterministic behavior.

Findings

Self-similar automata can perform hypercomputations.

Self-similar Petri nets can solve the halting problem.

The paper discusses indeterminism in self-similar cellular automata.

Abstract

We have recently introduced the two new computing models of self-similar cellular automata and self-similar Petri nets. Self-similar automata result from a progressive, infinite tessellation of space and time. Self-similar Petri nets consist of a potentially infinite sequence of coupled transitions with ever increasing firing rates. Both models are capable of hypercomputations and can, for instance, ``solve'' the halting problem for Turing machines. We survey the main definitions and propositions and add new results regarding the indeterminism of self-similar cellular automata.