Specifications and Modeling

How can we describe the system which we would like to design, and how can we represent intermediate design information? Models and description techniques for initial specifications as well as for intermediate design information will be shown in this chapter. First of all, we will capture requirements for modeling techniques. Next, we will provide an overview of models of computation. This will be followed by a presentation of popular models of computations, in combination with examples of the corresponding languages. The presentation includes models for early design phases, automata-based models, data flow, Petri nets, discrete event models, von Neumann languages, and abstraction levels for hardware modeling. Finally, we will compare different models of computation and present exercises.

Information Processing by Symmetric Inductive Turing Machines

Traditional models of computations, such as Turing machines or partial recursive functions, perform computations of functions using a definite program controlling these computations. This approach detaches data, which are processed, and the permanent program, which controls this processing. Physical computers often process not only data but also their software (programs). To reflect this peculiarity of physical computers, symmetric models of computations and automata were introduced. In this paper, we study information processing by symmetric models, which are called symmetric inductive Turing machines and reflexive inductive Turing machines.

Information Processing by Symmetric Inductive Turing Machines

Traditional models of computations, such as Turing machines or partial recursive functions, perform computations of functions using a definite program controlling these computations. This approach detaches data, which are processed, and the permanent program, which controls this processing. Physical computers often process not only data but also their software (programs). To reflect this peculiarity of physical computers, symmetric models of computations and automata were introduced. In this paper, we study information processing by symmetric models, which are called symmetric inductive Turing machines and reflexive inductive Turing machines.

Triadic Automata and Machines as Information Transformers

Algorithms and abstract automata (abstract machines) are used to describe, model, explore and improve computers, cell phones, computer networks, such as the Internet, and processes in them. Traditional models of information processing systems—abstract automata—are aimed at performing transformations of data. These transformations are performed by their hardware (abstract devices) and controlled by their software (programs)—both of which stay unchanged during the whole computational process. However, in physical computers, their software is also changing by special tools such as interpreters, compilers, optimizers and translators. In addition, people change the hardware of their computers by extending the external memory. Moreover, the hardware of computer networks is incessantly altering—new computers and other devices are added while other computers and other devices are disconnected. To better represent these peculiarities of computers and computer networks, we introduce and study a more complete model of computations, which is called a triadic automaton or machine. In contrast to traditional models of computations, triadic automata (machine) perform computational processes transforming not only data but also hardware and programs, which control data transformation. In addition, we further develop taxonomy of classes of automata and machines as well as of individual automata and machines according to information they produce.

A NEW MODEL FOR HETEROGENEOUS EMBEDDED SYSTEMS — What Esterel and SyncCharts Need to Become a Suitable Specification Platform

Specification of embedded systems based on formal models of computation is gaining importance. The behavior of an increasing number of embedded systems is heterogeneous, consisting of a mixture of control-dominated and data-dominated parts. While models of computations suitable to control-dominated systems and data-dominated systems are well developed, there are only a limited number of models catering to both systems. In this paper, we present informally a new model for heterogeneous embedded systems, called HEMOC, which combines three common models of computation, synchronous reactive, hierarchical finite state machines and synchronous data flow. Then, the languages Esterel and SyncCharts are used for system specification following the new model in order to determine what they need to become suitable specification platform.

Eduction

We know what a Lucid program means mathematically (see Chapter 3), yet that in itself does not suggest a particular model of computation for deriving the same meaning operationally. The purpose of this chapter is to consider the various ways that Lucid programs can be evaluated and to describe in detail the most appropriate model of computation, namely, eduction. Previously, we have seen that Lucid programs can be viewed globally in geometrical terms or locally in elemental terms. Both these views are equally valid as mental devices to enable the programmer to conceive and understand Lucid programs. And each view suggests its own family of computing models—extensional models that embody the global geometrical view and intensional models that embody the local elemental view. Before we compare these two approaches to evaluating Lucid programs, it is worth relating the operational semantics given by a model of computation to the mathematical semantics. Since Lucid is purely declarative, the correct meaning of a Lucid program is that which is given mathematically. This is done without appealing to any operational notions [8]. Thus, the mathematical semantics of a Lucid program has primacy over the many operational semantics that can be given to the Lucid program using different models of computations. Consequently, the correctness of a model of computation is determined by its ability to operationally give semantics to Lucid programs that coincide with their mathematical semantics. Let us consider an extensional model of computation called reduction [37]. It is the standard model for evaluating declarative programs, and more specifically, functional programs. In reduction, programs are considered to be expressions, and a program is evaluated by repeatedly transforming, or reducing, the expression into a possibly simpler expression. The original expression must include any data that the program is to work on, so that at every stage we are manipulating both program and data, and the two become intimately entwined. The process stops when no further transformation can be applied. At each stage, several transformations may be possible, but it doesn’t matter which we apply. If we get an answer, we always get the same answer, but it is possible to make choices so that we do not arrive at the answer.