Up until now classical logic has been the logic of choice in formal hardware verification. This report advances the application of intuitionistic logic to the timing analysis of digital circiuts. The intuitionistic setting serves two purposes at the same time. The model-theoretic properties are exploited to handle the second-order nature of bounded delays in a purely propositional setting without need to introduce explicit time and temporal operators. The proof theoretic properties are exploited to extract quantitive timing information and to reintroduce explicit time in a convenient and systematic way.
We present a natural Kripke-style semantics for intuitionistic propositional logic, as a special case of a Kripke constraint model for Propositional Lax Logic [4], in which validity is validity up to stabilization. We show that this semantics is equivalently characterized in terms of stabilization bounds so that implication comes out as "boundedly gives rise to." An intensional semantics for proofs is presented which allows us effectively to compute quantitative stabilization bounds.
We discuss the application of the theory to the timing analysis of combinational circiuts. To test our ideas we have implemented an experimental prototype tool and run several simple examples.
Ulrike Peiker, Martin Griebl