On breakable cyclic definitions

In the course of hardware system design or real-time process control, high-level specifications may contain simultaneous definitions of concurrent modules whose information flow forms cyclic dependencies without the separation of state-holding elements. The temporal behavior of these cyclic definitions may be meant to be combinational rather than sequential. Most prior approaches to analyzing cyclic combinational circuits were built upon the formulation of ternary-valued simulation at the circuit level. This work shows the limitation of this formulation and investigates, at the functional level, the most general condition where cyclic definitions are semantically combinational. It turns out that the prior formulation is a special case of our treatment. Our result admits strictly more flexible high-level specifications. Furthermore, it allows a higher-level analysis of combinationality, and, thus, no costly synthesis of a high-level description into a circuit netlist before combinationality analysis can be performed. With our formulation, when the target is software implementations, combinational cycles need not be broken as long as the execution of the underlying system obeys a sequencing execution rule. For hardware implementations, combinational cycles are broken and replaced with acyclic equivalents at the functional level to avoid malfunctioning in the final physical realization.