Complexity of Fungal Automaton Prediction

TL;DR

This paper investigates the computational complexity of predicting behaviors in fungal automata, revealing efficient predictability in most cases but proving P-completeness for certain rules at radius 1.5.

Contribution

It characterizes the complexity of all fungal automata rules of radius 1, identifying cases that are efficiently predictable and proving P-completeness for the freezing majority rule at radius 1.5.

Findings

Most fungal automata rules are predictably in non-deterministic logspace.

The freezing majority rule at radius 1.5 is P-complete to predict.

A non-linear rule remains open for complexity characterization.

Abstract

Fungal automata are a nature-inspired computational model, where a rule is alternatively applied verticaly and horizontaly. In this work we study the computational complexity of predicting the dynamics of all fungal freezing totalistic one-dimentional rules of radius $1$, exhibiting various behaviors. Despite efficiently predictable in most cases (with non-deterministic logspace algorithms), a non-linear rule is left open to characterize. We further explore the freezing majority rule (which is totalistic), and prove that at radius $1.5$ it becomes $\mathbf{P}$-complete to predict.