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

• Main Authors: Michael J. Dinneen, Yun-Bum Kim, Radu Nicolescu
• Format: Article
• Language: English
• Published: Open Publishing Association 2009-11-01
• Series: Electronic Proceedings in Theoretical Computer Science
• Online Access: http://arxiv.org/pdf/0911.4986v1

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.