Abstract: In this paper, we try to find new reflections of Flownomial Calculus in Computer Science world. Flownomial Calculus is an abstract calculus for networks seen as directed labelled hypergraphs. We work with flownomial expressions obtained by a repeated application of juxtaposition, composition and feedback operations over basic elements like variables and connections. Using this formalism, we could model flowcharts, graphs, relations, dataflows, circuits etc.

This thesis is divided into three parts, gradually passing from theory to practice, as the chosen title suggests.

First part is a succinct presentation of flownomial calculus. We begin with basic definitions, BNA axiom set; then we describe an algebra of relations, a normal form associated to an expression and simulation via bijections, and we end with the additive, multiplicative and mixed models for this algebraic framework.

In the second part we apply the theory of flownomials for modeling some concepts from Computer Science, first graphs and then classes and objects from object-oriented programming field. For graphs, we offer algorithms to obtain the flownomial expression associated to a graph and also to build the graph associated to an expression. To specify a class, we put its information in one mixed flownomial expression, additively juxtaposing methods and attributes, and then applying a multiplicative feedback. An object of a class will be a typed value kept in the feedback connection of its class.

Third part describes a Java implementation of flownomial expression. Using the Flow applet, one can easily compute and see the normal form of a flownomial expression and also to test the equivalence (similarity via bijections) of two expressions.

Full paper - 270 K (in Romanian)

Slides - 85 K (in Romanian)

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