On the characterization of until as a fixed point under clocked semantics

Modern hardware designs are typically based on multiple clocks. While a singly-clocked hardware design is easily described in standard temporal logics, describing a multiply-clocked design is cumbersome. Thus, it is desirable to have an easier way to formulate properties related to clocks in a temporal logic. In [6] a relatively simple solution built on top of the traditional ltl semantics was suggested and adopted by the IEEE standard temporal logic psl. The suggested semantics was examined relative to a list of design goals, and it was shown that it answered all requirements except for preserving the least fixed point characterization of the until operator under multiple clocks. In this work we show that with a minor addition to the semantics of [6] this requirement is met as well.