2.1.2.  Gajski-Kuhn chart

A more detailed abstraction model is the Y-chart Gajski and Kuhn invented in 1983, well explained in [DH99]. With this well-known chart it is possible to visualize design views as well as design hierarchies. It is widely used within VHDL design and can give us an idea for modeling abstraction levels, too. The name Y-chart arises from the three different design views, which are shown as radial axes forming a ‘Y’.


Figure 2.1: Gajski-Kuhn Y-chart, pursuant to [DH99, p. 358]

Five concentric circles characterize the hierarchical levels within the design process, with increasing abstraction from the inner to the outer circle. Each circle characterizes a model, explained after introducing the three domains.

This domain describes the temporal and functional behavior of a system.
A system is assembled from subsystems. Here the different subsystems and their interconnection to each other is contemplated for each level of abstraction.
Important in this domain are the geometric properties of the system and its subsystems. So there is information about the size, the shape and the physical placement. Here are the restrictions about what can be implemented e. g. in respect of the length of connections.

With these three domains the most important properties of a system can be well specified. The domain axes intersect with the circles that show the abstraction levels. The five circles from highest to lowest level of abstraction are (outer to inner circles):

A system’s requirements and its basic concepts for meeting the requirements are specified here.
The “how” aspect of a solution is refined. Functional descriptions about how the different subsystems interact, etc. are included.
Functional block or register-transfer.

Detailed descriptions of what is going on, from what register over which line to where a data is transferred, is the contents of this level.

The single logic cell is in the focus here, but not limited to AND, OR gates, also Flip-Flops and the interconnections are specified.
This is the actual hardware level. The transistor with its electric characteristics is used to describe the system. Information from this level printed on silicon results in the chip.


Figure 2.2: Design Levels, [DH99, p. 358]

A good illustration of the abstraction levels is Figure  2.2 on page 27. I personally like this taxonomy, as it shows how the word abstraction can be seen from different point of views. It is a refined model but simple enough to get an overview on one eye shot.

Keeping in mind that the Gajski-Kuhn chart was created in 1983, you can see that the ideas of [BR01] are not totally new, their achievement was more to transfer the approach of Gajski and Kuhn to the automotive sector and to determine the possibility of using modeling languages like UML for the problem.