The purpose of this thesis is to introduce proposition-oriented behaviours and apply them to the verification of asynchronous circuits. The major contribution of propositionoriented behaviours is their ability to extend existing formal notations to permit the explicit use of both signal levels and transitions. This thesis begins with the formalisation of proposition-oriented behaviours in the c...

Proposition 2. A is restricted weak-type (pd, qd). Proof (Proposition 2 ⇒ Theorem 1). Proposition 2 corresponds to an estimate at the vertex Pd of the trapezium. Since A and the adjoint operator A ∗ have the same mapping properties, one concludes there is a restricted weak-type estimate for the exponents corresponding to the vertex P ′ d. By localisation we know A is type (1, 1) and type (∞,∞) ...