On the size of PLA's required to realize binary and multiple-valued functions

This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.IEEE Transactions on Computers, C-38, Jan. 1989, pp. 82-98, 1988While the use of programmable logic arrays in modern logic design is common, little is known about what PLA size provides reasonable coverage in typical applications. We address this question by showing upper and lower bounds on the average number of product terms required in the minimal realization of binary and multiple-valued functions as a function of the number of nonzero output values. When the number of such values is small, the bounds are nearly the same, and accurate values for the average are obtained. In addition, an upper bound is derived for the variance of the distribution of the number of product terms required in minimal realizations of binary functions. When the number of nonzero values is small, we find that the variance is small, and it follows that most functions require nearly the average number of product terms. The variance, in addition to the upper and lower bounds, allow conclusions to be made about how PLA size determines the set of realizable functions. Although the bounds are most accurate when there are few nonzero values, they are adequate for analyzing commercially available PLA’s, which we do in this paper. Most such PLA’s are small enough that our results can be applied. For example, when the number of nonzero values exceeds some threshold uT, determined by the PLA size, only a small fraction of the functions can be realized. Our analysis shows that for all but one commercially available PLA, the number of nonzero values is a statistically meaningful criteria for determining whether or not a given function is likely to be realized

Delayed colorectal cancer care during covid-19 pandemic (decor-19). Global perspective from an international survey

Background The widespread nature of coronavirus disease 2019 (COVID-19) has been unprecedented. We sought to analyze its global impact with a survey on colorectal cancer (CRC) care during the pandemic. Methods The impact of COVID-19 on preoperative assessment, elective surgery, and postoperative management of CRC patients was explored by a 35-item survey, which was distributed worldwide to members of surgical societies with an interest in CRC care. Respondents were divided into two comparator groups: 1) ‘delay’ group: CRC care affected by the pandemic; 2) ‘no delay’ group: unaltered CRC practice. Results A total of 1,051 respondents from 84 countries completed the survey. No substantial differences in demographics were found between the ‘delay’ (745, 70.9%) and ‘no delay’ (306, 29.1%) groups. Suspension of multidisciplinary team meetings, staff members quarantined or relocated to COVID-19 units, units fully dedicated to COVID-19 care, personal protective equipment not readily available were factors significantly associated to delays in endoscopy, radiology, surgery, histopathology and prolonged chemoradiation therapy-to-surgery intervals. In the ‘delay’ group, 48.9% of respondents reported a change in the initial surgical plan and 26.3% reported a shift from elective to urgent operations. Recovery of CRC care was associated with the status of the outbreak. Practicing in COVID-free units, no change in operative slots and staff members not relocated to COVID-19 units were statistically associated with unaltered CRC care in the ‘no delay’ group, while the geographical distribution was not. Conclusions Global changes in diagnostic and therapeutic CRC practices were evident. Changes were associated with differences in health-care delivery systems, hospital’s preparedness, resources availability, and local COVID-19 prevalence rather than geographical factors. Strategic planning is required to optimize CRC care