A Canonical Form for Affine Relations in Signal

In this paper we present affine transformations as an extension of the Signal language for the specification and validation of real-time applications. A Signal program is a system of equations which specify dependencies between program data and synchronization constraints on clock variables. In order to test if a program is functionally safe, the Signal compiler resolves the clock constraints and verifies that the data dependency graph contains no cycles. By means of the new transformations, affine relations can be defined between clock variables and it gets necessary to enhance the compiler with facilities for the resolution of synchronization constraints on these clocks. To tackle these constraints, we propose an extension of the compiler based essentially on a canonical form of the affine relations. This extension removes some of the limits of the existing compiler and enlarges the range of applications that can be validated using Signal