# Timed Boolean Functions: A Unified Formalism for Exact by William K.C. Lam, Robert K. Brayton

By William K.C. Lam, Robert K. Brayton

Timing learn in excessive functionality VLSI platforms has complicated at a gentle speed over the past few years, whereas instruments, in particular theoretical mechanisms, lag in the back of. a lot current timing learn is based seriously on timing diagrams, which, even supposing intuitive, are insufficient for research of enormous designs with many parameters. additional, timing diagrams provide simply approximations, now not detailed ideas, to many timing difficulties and supply little perception within the circumstances the place temporal houses of a layout engage intricately with the design's logical functionalities. This ebook provides a technique for timing study which enables analy­ sis and layout of circuits and platforms in a unified temporal and logical area. within the first half, we introduce an algebraic illustration formalism, Timed Boolean services (TBF's), which integrates either logical and timing informa­ tion of electronic circuits and structures right into a unmarried formalism. We additionally supply a canonical shape, TBF BDD's, for them, which are used for effective ma­ nipulation. within the moment half, we follow Timed Boolean features to 3 difficulties in timing examine, for which distinct recommendations are acquired for the 1st time: 1. computing the precise delays of combinational circuits and the minimal cycle instances of finite kingdom machines, 2. research and synthesis of wavepipelining circuits, a excessive pace structure for which unique timing kin among signs are crucial for proper operations, three. verification of circuit and approach functionality and insurance of hold up faults via testing.

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Additional resources for Timed Boolean Functions: A Unified Formalism for Exact Timing Analysis

Example text

That is, the output y(t) is related to the input x(t) through the equation y(t) = x(t - d). Obviously, y(t) = x(t - d) gives the correct output value of the buffer at t; and further if the last input transition occurs at t = 0, then the settling time for the buffer is d. Denote the steady state input and output by x and fj, respectively. e. the steady state input; hence, for t ~ d, y(t) = x(t - d) reduces to the ordinary Boolean function for a buffer, namely fj = x. Based on this simple observation, we generalize and fonnalize this concept.

An essential prime of f if it contains a minterm of f not contained in any other prime. A cover K is a Boolean function 2::i Ci where Ci is a cube. Also, a representation of a Boolean function by a sum of cubes is called a sum of products or two-level representation, because it corresponds to a two-level AND-OR circuit implementation. In contrast to two-level representation, a multi-level representation, or factored form, is a parenthesized algebraic expression, which corresponds to a multi-level network.

Timed Boolean Functions 41 Once a k-BDD for the intervals is constructed, replace each leaf node with the node of the multi-rooted BDD corresponding to the interval of the leaf node. For the dummy intervals, the leaf nodes may point to a don't-care BDD node or the BDD's of neighboring leaf nodes as to simplify the overall BDD. 2 Canonical k-BDD Building a k-BDD from a set of intervals is as discussed above. It may be convenient to construct a k-BDD directly from, say, a circuit without first deriving a set of intervals.