A Theory of Binary Signal

The dynamic modelling of logical systems widely calls upon the explicit use of time and the event notion. In terms of Function Chart Grafcet or Interpreted Petri Nets for instance, events are generally represented by " rising or falling edges " of logical variables. However, numerous ambiguities are encountered in the models because the translation of events into edges is not formal enough. In this paper, we propose a theory of binary signal which allows us to describe the time behavior of the inputs and the outputs of any logical system. We especially describe an extended Boolean Algebra. In this algebra, we have defined two unary operations in order to formally express the events. Then, we give ten properties related to these rising and falling edge operations and their composition with the operations AND, OR, and NOT.