Mathias Halbach

Implementing cellular automata in FPGA logic

Summary form only given. We have searched for a performance platform to run billions of simulations in the cellular automata model for optimizing applications. The question was how much speed-up could be gained by using the FPGA technology compared to optimized software. We have implemented to cellular automata rules in software on a PC and in hardware. On our low end experimental platform we reached a speed-up of 3 for a medium complex rule and 22 for a complex rule. If we would use the latest high end FPGA technology, speed-ups up to many thousand are realistic. A cluster of thousands of workstations would be necessary to reach the same performance, which is much more costly than the FPGA solution.

Optimal 6-state algorithms for the behavior of several moving creatures

The goal of our investigation is to find automatically the absolutely best rule for a moving creature in a cellular field The task of the creature is to visit all empty cells with a minimum number of steps We call this problem creatures exploration problem The behaviour was modelled using a variable state machine represented by a state table Input to the state table is the current state and the neighbours state in front of the creatures moving direction The problem is that the search space for the possible rules grows exponentially with the number of states, inputs and outputs We could solve the problem for six states, two inputs and two outputs with the aid of a parallel hardware platform (FPGA technology) The set of all possible n-state algorithms was first reduced by discarding equivalent, reducible and not strongly connected ones The algorithms which showed a certain performance for five initial configurations during simulation were extracted by the hardware and send to the host PC Additional tests for robustness and the behaviour of several creatures was carried out in software One creature with the best algorithm can visit 99.92 % of the empty cells of 26 test configurations Several creatures up to 16 can perform the task more efficiently for the tested initial configuration.

Optimizing the behavior of a moving creature in software and in hardware

We have investigated a problem where the goal is to find automatically the best rule for a cell in the cellular automata model. The cells are either of type OBSTACLE, EMPTY or CREATURE. Only CREATURE can move around in the cell space in one changeable direction and can perform four actions: if the path to the next cell is blocked turn left or right, if the path is free, i. e. the neighbor cell is of type EMPTY: move ahead and simultaneously turn left or right. The task of the creature is to cross all empty cells with a minimum number of steps.

Optimal behavior of a moving creature in the cellular automata model

The goal of our investigation is to find automatically the best rule for a cell in the cellular automata model. The cells are either of type Obstacle, Empty or Creature. Only Creature can move around in the cell space and can perform one of the four actions: if the path to the next cell is blocked: turn left or right, if the path is free: move ahead and simultaneously turn left or right. The task of the creature is to cross all empty cells with a minimum number of steps. The behavior was modeled using a variable state machine represented by a state table. Input to the state table is the neighbors state in front of its moving direction. The goal is to find the absolutely best rule in the set of all possible rules. The search space grows exponentially with the number of states. As simulation, testing and evaluating the quality are very time consuming in software, the migration of the problem to a parallel hardware platform is a promising solution. In order to reduce the computation time, the search procedure was (1) implemented in hardware and (2) solutions which are equivalent under state permutations were not generated and (3) solutions which show or expect bad or trivial behavior were excluded as soon as possible in a preselection phase. Exactly six different five-state algorithms could be detected, which allow to cross all empty cells for all the given initial configurations. We described this model in Verilog HDL and in AHDL. A hardware synthesizing tool transforms the description into a configuration file which was loaded into a field programmable gate array (FPGA). Hardware implementation offers a significant speed up of many thousands compared to software.

Implementation of the Massively Parallel Model GCA

The GCA (Global Cellular Automata) model is a very interesting model which can be used to implement all kind of parallel problems. The GCA model consists of a field of cells as in the Cellular Automata model. Each cell has links to a set of remote cells which can be dynamically changed from generation to generation. A cell reads the remote neighbours states and then changes its own state according to a local rule. The model is massively parallel because all cells can change their states independently in parallel. We have investigated how the GCA model can be implemented efficiently in hardware using a FPGA prototyping platform. We have implemented a fully parallel architecture where all cells really operate in parallel and another architecture where the cells are stored in memories in order to handle a large number of cells. We are showing that in the fully parallel architecture a speed-up of more than 3000 compared to a software implementation on a PC is realistic on a modern FPGA platform. In the partially parallel architecture based on memories the speed-up will be lower but the number of cells is only restricted by the capacity of the memories.

Are several creatures more efficient than a single one

We are presenting results from our project “Creatures exploration problem” The problem is the following: p creatures move around in an environment in order to visit all reachable empty cells in shortest time All creatures behave according to the same rule.

Solving the exploration's problem with several creatures more efficiently

We are presenting results of the creatures exploration problem with several creatures. The task of the creatures is to visit all empty cells in an environment with obstacles in shortest time and with a maximum of efficiency. The cells are arranged in a regular 2D grid and the underlying processing model is a Cellular Automaton (CA). We have investigated the question how many creatures and which algorithm should be used in order to fulfill the task most efficiently with lowest cost. We use a set of 10 different behaviors (algorithms) for the creature which have proved to be very efficient in the case where only one creature explores the environment. These algorithms were found by exhaustive search and evaluation by the aid of hardware (FPGA) implementation. Different environments and a varying number (1 to 64) of creatures were used in simulations in order to evaluate the cooperative work and efficiency. It turned out that for each environment a certain number of creatures and a certain algorithm is cost optimal in terms of work units. The total amount of work using one creature with the best algorithm X is many cases higher than the work using n creature with an adequate algorithm Y. Using several creatures, positive conflicts arise which may help to solve the problem more efficiently.