Abstract
First, I will complete the treatment of cyclic circuits by addressing the semantic and algorithmic approach using ternary logic (by Kleene and Scott), which gives a natural semantic vision of constructive Boolean logic. I'll show that a simple encoding of ternary values by pairs of Booleans leads to a symbolic algorithm for detecting the constructiveness of a cyclic circuit using BDDs(Binary Decision Diagrams), as well as to the construction of an equivalent acyclic circuit. Finally, I will show how to apply a symbolic calculation of the same type to the constructive correction of a sequential circuit (with memories) by a temporal exploration of its states, which is indispensable in practice and will be illustrated by the treatment of the examples shown in the previous lectures. This will complete the study of the logical and electrical constructivity of circuits by introducing the interplay of time between successive states in addition to the interplay of time within each state.
In the second part, I'll present an elegant and efficient mesochronous synchronizer (same-frequency clocks with constant phase shift) by J.-M. Chabloz and Ahmed Hemani (KTH Stockholm), and briefly explain how to make it plesiochronous (non-constant phase shift).
The end of the lecture will be devoted to the PTides model by Edward Lee et al, integrated into the Ptolemy system presented in the lecture on March 19. This model makes it easy to create distributed real-time implementations of complex programs by composing time-guaranteed circuits, programs and networks using an elegant timestamping method.
