S. Chakraborty, "Polynomial-time techniques for approximate timing analysis of asynchronous systems," Ph.D. dissertation, Stanford Univ., 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....wire forks, burst mode assumes fundamental mode (the circuit will stabilize internally before new inputs arrive) and bundled data assumes that all data is stable before the handshake signal arrives. Ensuring that the timing assumptions hold in timed design, such as burst mode, can be challenging [12]. The design style we investigated explicitly specifies theeffect of delays in a circuit in terms of assertions on relative ordering 1063 8210 03 17.00 2003 IEEE of events (e.g. goes high before goes low) Our application of relative timing is based on the unbounded delay model commonly used by ....

S. Chakraborty, "Polynomial-time techniques for approximate timing analysis of asynchronous systems," Ph.D. dissertation, Stanford Univ., 1998.

....In performance analysis and probabilistic timing verification, however, component delays are considered random variables and distributions or moments of time separations are of interest. There is a rich body of work on analyzing time separation of events in systems with bounded component delays [6, 2, 10, 18, 13, 4]. In [1] Hulgaard and Amon described a method for analyzing time separation of events with symbolic delays. Williams analyzed the latency and throughput of pipelines in [14] Algorithms for estimating the average performance of asynchronous circuits from average component delays were This work ....

....B[i; f ] and B[j; f ] are also needed to compute C[f; s] 0,0 0,1 0,2 0,3 1,0 1,1 1,2 1,3 2,0 2,1 2,2 2,3 3,0 3,1 3,2 3,3 Layer 0 Layer 1 Layer 2 Layer 3 Figure 5. Layers of a matrix. These dependencies suggest a layer wise computation of matrices A, B and C, similar to that used in [4]. To recapitulate, all events are assumed to be topologically indexed. Thus, if events i and j are predecessors of event f in the timing constraint graph, then i f and j f . Layer f of a matrix, say A, is composed of elements A[f; s] and A[s; f ] with s f . An n n matrix can thus be viewed ....

S. Chakraborty. Polynomial-Time Techniques for Approximate Timing Analysis of Asynchronous Systems. PhD thesis, Stanford University, Aug. 1998.

....Fig. 5. By hypothesis, the matrix entries used in these expressions are upper bounds of the corresponding maximum achievable time separations. Therefore, by Observations 1 and 2 of Section IV A, the newly computed value of (i; j) is an upper bound of (i; j) It has been further shown in [41] that the bounds computed by algorithm AcyclicApproxSep are exact if (i) the timing constraint graph has a single source event, and (ii) all events are of the same type (either all max or all min) We omit the proof here due to lack of space, and also because the result is not directly relevant to ....

S. Chakraborty, Polynomial-Time Techniques for Approximate Timing Analysis of Asynchronous Systems, Ph.D. thesis, Stanford University, Aug. 1998.

....represents an upper bound on the time separation from event u to event v. Since subgraph G 1 is acyclic, an algorithm for analyzing acyclic timing constraint graphs suffices to compute the entries of the Delta matrix. For the current work, the AcyclicApproxSep algorithm of Chakraborty and Dill [34], outlined in Fig. 3, is used for this purpose. 1 Since G 1 lies between cutsets C 1 and C 2 , the source events of G 1 are elements of cutset C 1 . Therefore, in order to apply algorithm AcyclicApproxSep to G 1 , the values of Delta(a 1 ; b 1 ) for every pair of events a 1 and b 1 in C 1 ....

....In general, setting the upper bound of the time separation between every pair of source events to 1 can lead to the computed bounds between other pairs of events to be 1 as well. However, this is not the case in tightly coupled systems, as shown below. 1 Details of the algorithm may be found in [34]. G is an acyclic timing constraint graph; n = total no. of events; m = no. of source events (no incoming edges) Source events have indices 0 through m Gamma 1, other events have indices m through n Gamma 1. preds(i) set of events with an edge to event i. ....

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S. Chakraborty, Polynomial-Time Techniques for Approximate Timing Analysis of Asynchronous Systems, Ph.D. thesis, Stanford University, Aug. 1998. 15

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