Reasoning about analog-level implementations of digital systems

An approach is described for specifying and reasoning about implementations of digital systems that are described at the analog level of abstraction. It is an extension of existing methods that use higher-order logic for reasoning about implementations described in terms of ideal components at the digital level of abstraction. The behaviour of analog components (transistors, etc) are conservatively specified by predicates on the analog voltages and currents at their terminals. A syntactically defined class of specifications is identified that has been found both to be adequately expressive and also to possess computationally tractable decision procedures. The overall approach is illustrated by deriving the conditions for correctness and for compositionality of TTL implementations of logic gates.