New Solutions to the Firing Squad Synchronization Problems for Neural and Hyperdag P Systems

TL;DR

This paper introduces two new solutions to the Firing Squad Synchronization Problem for hyperdag and neural P systems, achieving synchronization without membrane polarizations or conditional rules, and applicable to general digraphs.

Contribution

The paper presents the first uniform solutions for FSSP in hyperdag and neural P systems with anonymous cells, extending beyond tree-based structures and using only states and classical rules.

Findings

Solution based on dynamic extension with mobile channels is faster.

Second solution uses only static channels and classical rules.

Both solutions work for any subset of the underlying digraphs.

Abstract

We propose two uniform solutions to an open question: the Firing Squad Synchronization Problem (FSSP), for hyperdag and symmetric neural P systems, with anonymous cells. Our solutions take e_c+5 and 6e_c+7 steps, respectively, where e_c is the eccentricity of the commander cell of the dag or digraph underlying these P systems. The first and fast solution is based on a novel proposal, which dynamically extends P systems with mobile channels. The second solution is substantially longer, but is solely based on classical rules and static channels. In contrast to the previous solutions, which work for tree-based P systems, our solutions synchronize to any subset of the underlying digraph; and do not require membrane polarizations or conditional rules, but require states, as typically used in hyperdag and neural P systems.