Tabular Documentation of Interactive Deterministic Systems derived from Algebraic Models

Many reactive deterministic systems have a simple algebraic model consisting of a set S of states, a set C of commands the system may receive and a state transition function n : S C ! S that can be extended to operate over streams. We study decompositions of the state transition function using de nition-by-cases organised around mode sets and system actions. We show how these decompositions can be documented by tabular displays developed by D. L. Parnas and coworkers. We consider how a tree structure can be used to organise such decompositions and describe how tabular displays are derived by the use of nesting. By restricting the construction of the tree two special cases are identi ed that are useful for decomposing the behaviour of interactive systems. To illustrate these techniques three examples are included: a word processor, a pocket calculator and a compact disk player. To analyse the tabular displays of the decompositions we analyse the underlying formal model of computation. We consider the computational power of nite tabular algebraic decompositions and the problem of determining the completeness and consistency of such decompositions. E-mail: [email protected]