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Design disjunction is developed to offer a broad coverage, high resolution, and low overhead approach to online diagnosis and recovery of reconfigurable fabrics. Design disjunction leverages the condensed diagnosability of <inline-formula><tex-math notation="LaTeX">$T$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq1-2513762.gif"/></alternatives></inline-formula> logic resources to achieve self-recovery using partial reconfiguration in O(log <inline-formula><tex-math notation="LaTeX">$T$ </tex-math><alternatives><inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq2-2513762.gif"/></alternatives></inline-formula>) steps. Reconfiguration is guided by the constructive property of <inline-formula><tex-math notation="LaTeX"> $f$</tex-math><alternatives><inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq3-2513762.gif"/></alternatives> </inline-formula>-disjunctness which forms O(log <inline-formula><tex-math notation="LaTeX">$T$</tex-math> <alternatives><inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq4-2513762.gif"/></alternatives></inline-formula>) resource groups at design-time. Resolution of <inline-formula><tex-math notation="LaTeX">$f$</tex-math> <alternatives><inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq5-2513762.gif"/></alternatives></inline-formula> simultaneous resource faults is shown to be guaranteed when the resource groups are mutually <inline-formula> <tex-math notation="LaTeX">$f$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq6-2513762.gif"/></alternatives></inline-formula>-disjunct.&#x00A0;This extends run-time fault resilience to a large resource space with certainty for up to <inline-formula> <tex-math notation="LaTeX">$f$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq7-2513762.gif"/></alternatives></inline-formula> faults using a decision-free resolution process that also provides a high likelihood of identifying the fault&#x2019;s location to a fine granularity. Finally, design disjunction is parameterized to accommodate the low coverage issue of functional testing for which inarticulate tests can otherwise impair fault isolation. Experimental results for MCNC and ISCAS benchmarks on a Xilinx 7-series field programmable gate array&#x00A0;(FPGA) demonstrate <inline-formula><tex-math notation="LaTeX"> $f$</tex-math><alternatives><inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq8-2513762.gif"/></alternatives> </inline-formula>-diagnosability at the individual slice level with a minimum average isolation accuracy of <inline-formula><tex-math notation="LaTeX">$96.4$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq9-2513762.gif"/></alternatives></inline-formula>&#x00A0;percent (<inline-formula> <tex-math notation="LaTeX">$94.4$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq10-2513762.gif"/></alternatives></inline-formula> percent) for <inline-formula> <tex-math notation="LaTeX">$f=1$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq11-2513762.gif"/></alternatives></inline-formula>&#x00A0;(<inline-formula> <tex-math notation="LaTeX">$f=2$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq12-2513762.gif"/></alternatives></inline-formula>). Results have also demonstrated millisecond order recovery with a minimum increase of <inline-formula><tex-math notation="LaTeX"> $83.6$</tex-math><alternatives><inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq13-2513762.gif"/></alternatives> </inline-formula> percent in fault coverage compared to <inline-formula><tex-math notation="LaTeX">$N$ </tex-math><alternatives><inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq14-2513762.gif"/></alternatives></inline-formula> -modular redundancy&#x00A0;(NMR) schemes. Recovery is achieved while incurring an average critical path delay impact of only <inline-formula><tex-math notation="LaTeX">$1.49$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="alzahrani-ieq15-2513762.gif"/></alternatives></inline-formula> percent and energy cost roughly comparable to conventional two-MR approaches.

Fast Online Diagnosis and Recovery of Reconfigurable Logic Fabrics Using Design Disjunction