The problem of mathematically modeling computation may at first seem insurmountable: Throughout history people have been solving computational tasks using a wide variety of methods, ranging from intuition and “eureka” moments to mechanical devices such as abacus or sliderules to modern computers. Besides that, other organisms and systems in nature are also faced with and solve computational tasks every day using a bewildering array of mechanisms. How can you find a simple mathematical model that captures all of these ways to compute? The problem is even further exacerbated since in this book we are interested in issues of computational efficiency. Here, at first glance, it seems that we have to be very careful about our choice of a computational model, since even a kid knows that whether or not a new video game program is “efficiently computable” depends upon his computer's hardware.