We present a generic framework of UTP theories for describing systems whose behaviour is characterised by regular time-slots, compatible with the general structure of the Circus language [WC01a]. This “slotted-Circus” framework is parameterised by the particular way in which event histories are observable within a time-slot, and specifies what laws a desired parameterisation must obey in order for a satisfactory theory to emerge.
Two key results of this work are: the need to be very careful in formulating the healthiness conditions, particularly R2; and the demonstration that synchronous theories like SCSP [Bar93] do not fit well with the way reactive systems are currently formulated in UTP and Circus.
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