Much design effort toward a Sproull Counterflow Pipeline Processor has been focused on management of movements of Instructions and Results in the pipelines so that every Instruction and Result that pass one another meet and interact in exactly one stage of the pipeline. The full SCPP design problem poses other requirements as well, such as creation and deletion of items flowing in the pipelines, scheduling of execution of instructions only in stages with the required hardware, and high speed. Nevertheless, even a simplified version of the design problem that ignores the latter requirements has resisted synthesis using existing formal methods. At a workshop on Asynchronous VLSI Design held in Israel on March 20-22, 1995, Alain Martin of Caltech discussed his synthesis methodology and tools, which he claimed can translate almost any Communicating Sequential Process (CSP) program to a circuit by systematic procedure. Since our essential requirements for movement of Instructions and Results had been expressed by us as a 5-state FSM graph that is easily interpreted as a CSP program, we asked Martin to demonstrate how his method would be applied to this problem. At the suggestion of the workshop organizer, Dr. Ran Ginosar of the Technion, Dr. Huub Schols presented the challenge to all of the workshop attendees, and produced the careful documentation contained here. Several thoughtful responses to our challenge are cited in the list of references. They lead us to conclude that the problem that we have posed is indeed difficult and worthy of further study and analysis. Martin has declined to provide us with any information about a solution that he claimed to have found after the workshop.

For the original article see ibid., vol.25, no.4, pp.942-951 (Aug. 1990). In the above titled paper L.-S. Kim and R.W. Dutton used SPICE small-signal circuit simulation (SPICE AC command) to evaluate a metastability performance parameter, tau , and compared several latch and flip-flop designs. They suggest that small-signal simulation is much easier to carry out than large-signal simulation for me...

The introduction of nonlinear damping into computational simulations of stable active cochlear mechanical models has introduced instability in computational simulations of models used here. Nonlinear dynamical systems theory provides tools that give insight into the possible sources of such instability. Analysis of differential equations for a simplified cochlear mechanical model with a computer program (“AUTO” by Eusebius Doedel) suggests that the unstable behavior of earlier simulations is an artifact of the computations rather than an inherent feature of the differential equation model. [Work supported by NIH grants NS21592 and RR01379.]

Fourier analyses have been conducted upon period histograms of responses of single cochlear nerve fibers to a pair of phase‐locked, equal‐amplitude tones whose frequencies f1 and f2 in relation to the characteristic frequency (CF) of the nerve fiber under study are given by the ratio CF:f1:f2 = i:j:k, where i, j, and k are positive integers satisfying i<j<k and i = 2j−k (typically i = 10, j = 11, and k = 12). For moderate‐to‐high stimulus levels, the relative level of the 2f1−f2 component with respect to the primary components changes only slightly, which is consistent with the previous report by Goldstein and Kiang [Proc. IEEE 56, 981 (1968)]. Confirming the prediction of a nonlinear basilar‐membrane model which showed the above high‐level property of the distortion component 2f1−f2 as well as a smooth transition into effectively linear response characteristics for sufficiently low input levels [Kim et al., J. Acoust. Soc. Am. 53, 324 (1973)], we have observed that the 2f1−f2 component in cochlear nerve ...

A previously reported model for basilar-membrane motion [Kim et al., J. Acoust. Soc. Amer. 53 (1973)] generates many nonlinear phenomena observed in responses of single cochlear nerve fibers including combination tones (n+1)f1−nf2, where f1<f2, but does not account for other cochlear nerve nonlinear phenomena such as distortion components f2−f1, 2f1, f1+f2, and 2f2 which we have observed. Augmenting the basilar-membrane model by adding a noise waveform, rectification, and refractory effects produces a model with spike-discharge activity of single cochlear nerve fibers as the output and stapes displacement as the input. This model simulates (a) the linear response characteristics of spontaneously active cochlear nerve fibers at sufficiently low input levels (Littlefield et al., paper K5); (b) most of the nonlinear response characteristics of single cochlear nerve fibers at moderate-to-high input levels; (c) the smooth transition from the linear to the nonlinear response patterns; and (d) the observed lack of suppression of spontaneous activity by an externally applied tone. [This study was supported in part by grants from the U. S. Public Health Service.]

A phenomenological model for basilar membrane motion is presented. The model consists of 10 cascaded elements defined by the nonlinear differential equations ẍi(t) + 2Di[1 + ηẋi2(t)]ẋi(t) + ω0i2xi(t) = Cxi−1(t) for i = 1, 2, ⋯, 10, where x0(t) is the input (stapes displacement) and x10(t) is the output (displacement of a point on the basilar membrane). The model demonstrates a close relationship among seemingly disjoint nonlinear phenomena of the peripheral auditory system by showing the following response characteristics: (1) saturation of the output amplitude, decrease of Q, and decrease of the maximally responsive frequency with increase of input amplitude; (2) “amplitude” and “temporal” nonlinearities in response to combination clicks; (3) generation of combination tone 2f1 − f2 in response to inputs of two equal-amplitude tones (f1 < f2); (4) two-tone suppression for frequencies of the suppressing tone above the characteristic frequency; (5) change of the phase angle of the output with increasing amplitude of sinusoidal input; and (6) change of click response pattern with increasing click amplitude. The characteristic (1) has already been observed directly in basilar membrane motion. We suggest that the characteristics (2)–(6), which are similar to nonlinear phenomena observed in spike-discharge patterns of single cochlear nerve fibers, may actually be properties of basilar membrane motion.

We have obtained experimental evidence that the response activity of spontaneously active cochlear nerve fibers is effectively linear over a certain range of parameters. These results were obtained by examining the Fourier transforms of period histograms of discharge activity in response to one- and two-tone stimulation. The following four bounds describe a range of parameters in which the statistical response patterns of a cochlear nerve fiber in all experiments to date (more than 75 fibers) are consistent with a linear hypothesis: (1) stimulus frequency <2 kHz; (2) SL (stimulus level) <40 dB SPL; (3) A < Amax = (8/N)12 (where N is the total number of spike discharges in the histogram and A equals 2/N times the magnitude of the appropriate Fourier component); (4) the two tones must satisfy the constraint that the absolute difference between each SL (Amax)<20 dB. Linear responses have been obtained well outside this range, but no statistically significant nonlinear behavior has been witnessed inside this range with histograms having N = 8000 to 16 000 spikes. On the basis of these results, for example, we can conclude that no essential nonlinearities exist in this range. The latter conclusion is also supported by other data from this study that show that all distortion components measurable, f2−f1, f1+f1, 2f1, 2f2, 2f1−f2, 2f2−f1, etc., have been observed to fall off with decreasing stimulus level faster than the primaries f1 and f2. [This work was supported in part by grants from the U. S. Public Health Service.]

The CHASM is a "fixed plus variable" computer system composed of a specialized marcomodular processor coupled to a LINC. The CHASM is designed to carry out the analysis of a Markov process model for the time patterns of spike discharges of neurons. The fixed portion of the CHASM computes certain probabilities associated with the Markov process model. The LINC provides input and output for the fixed portion and controls the execution of the calculations. The bulk of the calculations is efficiently carried out by the fixed portion. The more irregular operations, which occur less frequently, are carried out by the LINC.

Responses of a mechanical model of the peripheral auditory system are calculated for two-tone stimuli with primary frequencies chosen so that the frequency of the cubic difference tone (2f1-f2) is maintained constant for all pairs used. The comprehensive model explicitly includes linear characterizations of the earphone driver, acoustic coupler, and middle ear, and a passive cochlear model with nonlinear damping of the cochlear partition motion. The amplitude and phase plots of the (2f1-f2) distortion signal, determined both in the ear canal and at the (2f1-f2) characteristic place, show rapid variations with f1, and quite different patterns depending on the stimulus level. These plots, as well as plots showing the spatial distribution of primary and distortion signals along the cochlea for six selected f1 values, are interpretable as showing interactions between multiple propagating waves at the distortion product frequency.