Kaisa Sere

Neural networks and genetic algorithms for bankruptcy predictions

Abstract We are focusing on three alternative techniques-linear discriminant analysis, logit analysis and genetic algorithms-that can be used to empirically select predictors for neural networks in failure prediction. The selected techniques all have different assumptions about the relationships between the independent variables. Linear discriminant analysis is based on linear combination of independent variables, logit analysis uses the logistical cumulative function and genetic algorithms is a global search procedure based on the mechanics of natural selection and natural genetics. In an empirical test all three selection methods chose different bankruptcy prediction variables. The best prediction results were achieved when using genetic algorithms.

Stepwise Refinement of Action Systems

A method for the formal development of provably correct parallel algorithms by stepwise refinement is presented. The entire derivation procedure is carried out in the context of purely sequential programs. The resulting parallel algorithms can be efficiently executed on different architectures. The methodology is illustrated by showing the main derivation steps in a construction of a parallel algorithm for matrix multiplication.

Superposition refinement of reactive systems

Superposition refinement enhances an algorithm by superposing one computation mechanism onto another mechanism, in a way that preserves the behavior of the original mechanism. Superposition seems to be particularly well suited to the development of parallel and distributed programs: an originally simple sequential algorithm can be extended with mechanisms that distribute control and state information to many processes, thus permitting efficient parallel execution of the algorithm. We will show in this paper how superposition of reactive systems is expressed in the refinement calculus. We illustrate the power of this method by a case study, showing how a distributed broadcasting system is derived through a sequence of superposition refinements.

Stepwise refinement of parallel algorithms

Abstract The refinement calculus and the action system formalism are combined to provide a uniform method for constructing parallel and distributed algorithms by stepwise refinement. It is shown that the sequencial refinement calculus can be used as such for most of the derivation steps. Parallelism is introduced during the derivation by refinement of atomicity. The approach is applied to the derivation of a parallel version of the Gaussian elimination method for solving simultaneous linear equation systems.

From Action Systems to Modular Systems

Action systems are used to extend program refinement methods for sequential programs, as described in the refinement calculus, to parallel and reactive system refinement. They provide a general description of reactive systems, capable of modeling terminating, possibly aborting and infinitely repeating systems. We show how to extend the action system model to refinement of modular systems. A module may export and import variables, it may provide access procedures for other modules, and it may itself access procedures of other modules. Modules may have autonomous internal activity and may execute in parallel or in sequence. Modules may be nested within each other. They may communicate by shared variables, shared actions, a generalized form of remote procedure calls and by persistent data structures. Both synchronous and asynchronous communication between modules is supported. The paper shows how a single framework can be used for both the specification of large systems, the modular decomposition of the system into smaller units and the refinement of the modules into program modules that can be described in a standard programming language and executed on standard hardware.

Hybrid action systems

In this paper we investigate the use of action systems with differential actions in the specification of hybrid systems. As the main contribution we generalize the definition of a differential action, allowing the use of arbitrary relations over model variables and their time derivatives in modelling continuous-time dynamics. The generalized differential action has an intuitively appealing predicate transformer semantics, which we show to be both conjunctive and monotonic. In addition, we show that differential actions blend smoothly with conventional actions in action systems even under parallel composition. Moreover, as the strength of the action system formalism is the support for stepwise development by refinement, we investigate refinement involving a differential action. We show that, due to the predicate transformer semantics, standard action refinement techniques apply also to the differential action, thus, allowing stepwise development of hybrid Systems.

An Approach to Object-Orientation in Action Systems

We extend the action system formalism with a notion of objects that can be active and distributed. With this extension we can model class-based systems as action systems. Moreover, as the introduced constructs can be translated into ordinary action systems, we can use the theory developed for action systems, especially the refinement calculus, even for class-based systems. We show how inheritance can be modelled in different ways via class refinement. Refining a class with an other class within the refinement calculus ensures that the original behavior of the class is maintained throughout the refinements. Finally, we show how to reuse proofs and entire class modules in a refinement step.

A Theory of Prioritizing Composition

An operator for the composition of two processes, where one process has priority over the other process, is studied. Processes are described by action systems, and data refinement is used for transforming processes. The operator is shown to be compositional, i.e. monotonic with respect to refinement. It is argued that this operator is adequate for modelling priorities as found in programming languages and operating systems. Rules for introducing priorities and for raising and lowering priorities of processes are given. Dynamic priorities are modelled with special priority variables which can be freely mixed with other variables and the prioritising operator in program development. A number of applications show the use of prioritising composition for modelling and specification in general.

Reasoning about Action Systems using the B-Method

The action system formalism has been succesfully used when constructing parallel and distributed systems in a stepwise manner within the refinement calculus. Usually the derivation is carried out manually. In order to be able to produce more trustworthy software, some mechanical tool is needed. In this paper we show how action systems can be derived and refined within the B-Toolkit, which is a mechanical tool supporting a software development method, the B-Method. We describe how action systems are embedded in the B-Method. Furthermore, we show how a typical and nontrivial refinement rule, the superposition refinement rule, is formalized and applied on action systems within the B-Method. In addition to providing tool support for action system refinement we also extend the application area of the B-Method to cover parallel and distributed systems. A derivation towards a distributed load balancing algorithm is given as a case study.

An Action System Approach to the Steam Boiler Problem

This paper presents an approach to the specification of control programs based on action systems and refinement. The system to be specified and its physical environment are first modelled as one initial action system. This allows us to abstract away from the communication mechanism between the two entities. It also allows us to state and use clearly the assumptions that we make about how the environment behaves. In subsequent steps the specifications of control program and the environment are further elaborated by refinement and are separated. We use the refinement calculus to structure and reason about the specification. The operators in this calculus allow us to achieve a high degree of modularity in the development.