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

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

A Minimal Time Solution to the Firing Squad Synchronization Problem with Von Neumann Neighborhood of Extent 2

Cellular automata provide a simple environment in which to study global behaviors. One example of a problem that utilizes cellular automata is the Firing Squad Synchronization Problem, first proposed in 1957. This paper provides an overview of the standard Firing Squad Synchronization Problem and a commonly used technique in solving it. This paper also provides a statement of a new extension of the Standard Firing Squad Synchronization Problem to a different neighborhood definition - a Von Neumann neighborhood of extent 2. An 8 state 651 rule minimal time solution to the extended problem is described, presented and proven, along with Python code used in running simulations of the solution

The Firing Squad Synchronization Problems for Number Patterns on a Seven-Segment Display and Segment Arrays

The Firing Squad Synchronization Problem (FSSP), one of the most well-known problems related to cellular automata, was originally proposed by Myhill in 1957 and became famous through the work of Moore [1]. The first solution to this problem was given by Minsky and McCarthy [2] and a minimal time solution was given by Goto [3]. A significant amount of research has also dealt with variants of this problem. In this paper, from a theoretical interest, we will extend this problem to number patterns on a seven-segment display. Some of these problems can be generalized as the FSSP for some special trees called segment trees. The FSSP for segment trees can be reduced to a FSSP for a one-dimensional array divided evenly by joint cells that we call segment array. We will give algorithms to solve the FSSPs for this segment array and other number patterns, respectively. Moreover, we will clarify the minimal time to solve these problems and show that there exists no such solution

A Genetically Evolved Solution to the Firing Squad Problem

In 1957, J. Myhill presented the firing squad problem. A special case of k-color cellular automata (CA) synchronization, the firing squad problem offers more stringent rules allowing for a provable minimal running time. To date, CA solutions have been found that run in minimal time using as many as sixteen states and as few as six [5]. There have also been arguments against the existence of solutions using only 4 states [11]. Due to the extremely large search space involved with such problems, the existing solutions have all been analytic in nature. We attempt to apply genetic algorithms and genetic programming to create transition tables that solve the firing squad problem. Ideally, the solutions would run in minimal time. No generalized solutions were found, but progress was made towards determining the best strategies for an evolved solution

Cartesian Knowledge and Confirmation

Bayesian conceptions of evidence have been invoked in recent arguments regarding the existence of God, the hypothesis of multiple physical universes, and the Doomsday Argument. Philosophers writing on these topics often claim that, given a Bayesian account of evidence, our existence or something entailed by our existence (perhaps in conjunction with some background knowledge or assumption) may serve as evidence for each of us. In this paper, I argue that this widespread view is mistaken. The mere fact of one's existence qua conscious creature cannot serve as evidence on the standard Bayesian conception of evidence because knowledge of one's existence is a necessary part of the background knowledge relative to which all epistemic probabilities are defined. It follows that some formulations of the fine-tuning argument (for theism or a multiverse), the argument from consciousness (for theism) and a rejoinder to the Doomsday argument are mistaken