This dissertation documents two contributions to automating the formal verification of hardware – particularly memory-intensive circuits – by Symbolic Trajectory Evaluation (STE), a model checking technique based on symbolic simulation over abstract sets of states. The contributions focus on improvements to the use of BDD-based STE, which uses binary decision diagrams internally. We introduce a solution to one of the major hurdles in using STE: finding suitable abstractions. Our work has produced the first known algorithm that addresses this problem by automatically discovering good, non-trivial abstractions. These abstractions are computed from the specification, and essentially encode partial input combinations sufficient for determining the specification’s output value. They can then be used to verify whether the hardware model meets its specification using a technique based on and significantly extending previous work by Melham and Jones [2]. Moreover, we prove that our algorithm delivers correct results by construction. We demonstrate that the abstractions received by our algorithm can greatly reduce verification costs with three example hardware designs, typical of the kind of problems faced by the semiconductor design industry. We further propose a refinement method for abstraction schemes when over- abstraction occurs, i.e., when the abstraction hides too much information of the original design to determine whether it meets its specification. The refinement algorithm we present is based on previous work by Chockler et al. [3], which selects refinement candidates by approximating which abstracted input is likely the biggest cause of the abstraction being unsuitable. We extend this work substantially, concentrating on three aspects. First, we suggest how the approach can also work for much more general abstraction schemes. This enables refining any abstraction allowed in STE, rather than just a subset. Second, Chockler et al. describe how to refine an abstraction once a refinement candidate has been identified. We present three additional variants of refining the abstraction. Third, the refinement at its core depends on evaluating circuit logic gates. The previous work offered solutions for NOT- and AND-gates. We propose a general approach to evaluating arbitrary logic gates, which improves the selection process of refinement candidates. We show the effectiveness of our work by automatically refining an abstraction for a content-addressable memory that exhibits over-abstraction, and by evaluating some common logic gates. These two contributions can be used independently to help automate the hard- ware verification by STE, but they also complement each other. To show this, we combine both algorithms to create a fully automatic abstraction discovery and refinement loop. The only inputs required are the hardware design and the specification, which the design should meet. While only small circuits could be verified completely automatically, it clearly shows that our two contributions allow the construction of a verification framework that does not require any user interaction.

Current return-to-drive recommendations for patients following rotator cuff repair (RCR) surgery are not uniform due to a lack of empirical evidence relating driving safety and time-after-surgery. To address the limitations of previous work, Badger et al. (2022) evaluated, on public roads, the driving fitness of patients prior to RCR and at multiple post-operative timepoints. The goal of the Badger, et al. study was to make evidence-based return-to-drive recommendations in an environment with higher fidelity than that of a simulator and not subject to biases inherent to surveys. Badger et al., however, do not fully investigate the driving practices exhibited by subjects, overlooking the potential presence of compensatory driver behaviors. Further investigation of these behaviors through observation of direct driving techniques and practices over time can specifically answer how drivers may modify their behaviors to address a perceived state of impairment. Additionally, the degree of success in vehicle operation by comparing an ideal turn to the path taken by the driver allows for a level of quantification of the effectiveness of the compensatory techniques. Moreover, driver trajectories inferred from the vehicle Controller Area Network (CAN) metrics and from global positioning system (GPS) coordinates are contrasted with the ideal turn to assess minimum requirements for future sensors that are used to make these trajectory comparisons. This investigation leverages pre-existing data collected by the Virginia Tech Transportation Institute (VTTI) and Carilion Clinic as used in the analysis performed by Badger et al. (2022). RCR patients (n=27) executed the same prescribed driving maneuvers and drove the same route in a preoperative state and at 2-, 4-, 6-, and 12-weeks post operation. Behavioral data were annotated to extract key characteristics of interest and related them to relevant vehicle sensor readings. To construct vehicle paths, data was obtained from the on-board data acquisition system (DAS). Behavioral metrics considered the use of ipsilateral vehicle controls, performance of non-primary vehicle tasks, and steering techniques utilized to assess the impact of mobility restrictions due to sling use. Sling use was found to be a significant factor in use of the non-ipsilateral hand associated with the operative extremity (i.e., operative hand) on vehicle functions and, in particular, difficulty with the gear shifting control. Additionally, when considering the performance of non-primary vehicle tasks as assessed through a prescribed visor manipulation, sling use was not a significant factor for the task duration or completion of the task in a fluid motion. Sling use was, however, significant with respect to operative hand position prior to the completion of the visor manipulation: the operative hand was often not on the steering wheel prior to the visor maneuver. In addition, the operative hand was never used to manipulate the visor when the sling was worn. One-handed steering was also more frequent with the presence of the sling. Further behavioral analysis assessed the presence of compensatory behavior exhibited by subjects during periods in which impairment was perceived. Perceived impairment was observed as a function of the different experimental timepoints. Findings indicated a significant decrease in the lateral vehicle jerk during post-operative weeks 6 and 12. Significant differences, however, were not observed in body position alteration to avoid contact with the interior vehicle cabin, in over-the-shoulder checks, and in forward leans during yield and merge maneuvers. Regarding trajectory analysis, sling use did not produce a significant difference in the error metrics between the actual and ideal paths. In completion of turning maneuvers, however, operative extremity was significant for left turns, with greater error against the ideal path observed from those in the left operative cohort compared to those in the right operative cohort. For the right turn, however, operative extremity was not found to be a significant factor. In addition, the GPS data accuracy proved insufficient to support comparison against the ideal path. Overall, findings from this study provide metrics beyond those used in Badger, et al. that can be used in answering when it is safe for rotator cuff repair patients to return-to-drive. With the limited differences observed as a function of study timepoint and sling use, it is recommended that patients are able to safely return-to-drive at two weeks post-operation. If anything, results suggest that overcompensation, as inferred from observation of safer driving behaviors than normal, is present during some experimental timepoints, particularly post-operative week 2. / Master of Science / Current recommendations based on when it is safe for rotator cuff repair patients to return-to-drive are not standard because of a lack of suitable evidence. Previous work and recommendations rely on surveys and simulators which do not create fully realistic conditions and are subject to biases. To address the limitations of previous work, Badger et. al (2022) studied actual rotator cuff repair patients on public roads prior and following operation at multiple timepoints. Badger et al., however, did not consider the potential adaptations in driver behavior due to mobility restrictions and the perception of inferiority due to injury. Additionally, the degree of success of the adaptive driving behaviors based on the error between the actual vehicle path taken and a defined ideal path have not been explored in conjunction with the injury. This investigation is based on the pre-existing data collected by the Virginia Tech Transportation Institute (VTTI) and Carilion Clinic as used in the analysis performed by Badger et al. (2022). RCR patients (n=27) executed identical driving maneuvers and drove the same route before operation and at 2-, 4-, 6-, and 12-weeks post operation. Behavioral observations were recorded and related to relevant vehicle sensor readings. To construct vehicle paths, data was taken from the on-board data acquisition system (DAS). Participants adopted different behaviors, such as using the right hand to use the turn signal when the left arm was in a sling and the left hand to operate the gear shifter when the right arm was on a sling, to assist in combating mobility restrictions. One-handed steering was also more prominent during periods of sling-use. Sling-use, however, did not produce a significant difference in error between the actual vehicle path taken and the ideal path available to the driver. For left-operated participants completing left turns, there was also greater error in comparison to the ideal path than for the group of right-operated patients. However, there was not a difference between left- and right-operated arm participant error in completion of a right turn. The GPS data did not provide a suitable approximation of vehicle trajectory. Overall, findings from this study help to answer when it is safe for rotator cuff repair patients to return-to-drive through evaluation of the effectiveness of compensatory behaviors adopted by participants. With no significant difference in turn execution based on sling use, results suggest that patients can safely return-to-drive at two weeks post-operation. In fact, results suggest that overcompensation towards safer behaviors is present during some experimental timepoints, particularly post-operative week 2.