Functional timing analysis of VLSI circuits containing complex gates

The recent advances in CMOS technology have allowed for the fabrication of transistors with submicronic dimensions, making possible the integration of tens of millions devices in a single chip that can be used to build very complex electronic systems. Such increase in complexity of designs has originated a need for more efficient verification tools that could incorporate more appropriate physical and computational models. Timing verification targets at determining whether the timing constraints imposed to the design may be satisfied or not. It can be performed by using circuit simulation or by timing analysis. Although simulation tends to furnish the most accurate estimates, it presents the drawback of being stimuli dependent. Hence, in order to ensure that the critical situation is taken into account, one must exercise all possible input patterns. Obviously, this is not possible to accomplish due to the high complexity of current designs. To circumvent this problem, designers must rely on timing analysis. Timing analysis is an input-independent verification approach that models each combinational block of a circuit as a direct acyclic graph, which is used to estimate the critical delay. First timing analysis tools used only the circuit topology information to estimate circuit delay, thus being referred to as topological timing analyzers. However, such method may result in too pessimistic delay estimates, since the longest paths in the graph may not be able to propagate a transition, that is, may be false. Functional timing analysis, in turn, considers not only circuit topology, but also the temporal and functional relations between circuit elements. Functional timing analysis tools may differ by three aspects: the set of sensitization conditions necessary to declare a path as sensitizable (i.e., the so-called path sensitization criterion), the number of paths simultaneously handled and the method used to determine whether sensitization conditions are satisfiable or not. Currently, the two most efficient approaches test the sensitizability of entire sets of paths at a time: one is based on automatic test pattern generation (ATPG) techniques and the other translates the timing analysis problem into a satisfiability (SAT) problem. Although timing analysis has been exhaustively studied in the last fifteen years, some specific topics have not received the required attention yet. One such topic is the applicability of functional timing analysis to circuits containing complex gates. This is the basic concern of this thesis. In addition, and as a necessary step to settle the scenario, a detailed and systematic study on functional timing analysis is also presented.