Analysis of a Mixed-Signal Circuit in Hybrid Process Algebra ACP(hs)(srt)

ACP(hs)(srt) is a hybrid process algebra obtained by extending a combination of two existing extensions of Algebra of Communicating Processes (ACP), namely the process algebra with continuous relative timing and the process algebra with propositional signals, for the formal specification and analysis of hybrid systems. In addition to equational axioms, this hybrid process algebra has rules to derive equations with the help of real analysis. ACP(hs)(srt) is also closely related to the theory of hybrid automata, so ACP(hs)(srt) can be reasonable easily translated to hybrid automata. This enables automatic verification of ACP(hs)(srt) specifications using existing hybrid automaton-based verification tools (e.g. PHAVer and HyTech). Since ACP(hs)(srt) is a well-developed algebraic theory from the field of hybrid process algebras with the above-mentioned features, it seems to allow rigorous the formal specification and analysis of digital/analog/mixed-signal circuits. In order to explore this fact, in this paper, we study a mixed-signal circuit: a half wave rectifier in ACP(hs)(srt). Some basic properties of the half wave rectifier are analysed in a formal way and some correctness requirements are also proven to be satisfied.