In this report we present a graphical tool, Behavioral Analysis of Spacecraft Systems (BASS), that can be used by spacecraft designers to perform system-level behavioral analysis of small satellites. The domain-specific spacecraft meta-model is created in the visual modeling tool Generic Modeling Environment (GME) such that spacecraft designs created using the meta-model appear familiar to the spacecraft designers. Users can model scenarios that are to be verified for the design in BASS. The graphical models are assigned formal semantics facilitating the creation of formally verifiable spacecraft models. The C++ application that translates the modeling objects to equivalent mathematical representation of interest is called BASS Interpreter and is bound to the meta-model. BASS Interpreter that generates Communicating Sequential Processes (CSP) semantics for the visual spacecraft models is supported in the current work. The model-checker for CSP called Failures Divergences and Refinement (FDR) is run to explore the state-space of the spacecraft process model to comment on the design. We demonstrate the feasibilty and advantage of incorporating BASS into initial design phases of small satellite development by successfully verifying the design of Tomographic Remote Observer of Ionospheric Disturbances (TOROID).

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In this dissertation, the concept of using domain specific language to develop errorree parallel asynchronous load scheduling protocols for distributed systems is studied. The motivation of this study is rooted in addressing the high cost of verifying parallel asynchronous load scheduling protocols. Asynchronous parallel applications are prone to subtle bugs such as deadlocks and race conditions due to the possibility of non-determinism. Due to this non-deterministic behavior, traditional testing methods are less effective at finding software faults. One approach that can eliminate these software bugs is to employ model checking techniques that can verify that non-determinism will not cause software faults in parallel programs. Unfortunately, model checking requires the development of a verification model of a program in a separate verification language which can be an error-prone procedure and may not properly represent the semantics of the original system. The model checking approach can provide true positive result if the semantics of an implementation code and a verification model is represented under a single framework such that the verification model closely represents the implementation and the automation of a verification process is natural. In this dissertation, a domain specific language based verification framework is developed to design parallel load scheduling protocols and automatically verify their behavioral properties through model checking. A specification language, LBDSL, is introduced that facilitates the development of parallel load scheduling protocols. The LBDSL verification framework uses model checking techniques to verify the asynchronous behavior of the protocol. It allows the same protocol specification to be used for verification and the code generation. The support to automatic verification during protocol development reduces the verification cost post development. The applicability of LBDSL verification framework is illustrated by performing case study on three different types of load scheduling protocols. The study shows that the LBDSL based verification approach removes the need of debugging for deadlocks and race bugs which has potential to significantly lower software development costs.

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The ideals of exact modeling, and of putting off approximations as long as possible, make Bayesian practice both successful and difficult. Languages for modeling probabilistic processes, whose implementations answer questions about them under asserted conditions, promise to ease much of the difficulty. Unfortunately, very few of these languages have mathematical specifications. This makes them difficult to trust: there is no way to distinguish between an implementation error and a feature, and there is no standard by which to prove optimizations correct. Further, because the languages are based on the incomplete theories of probability typically used in Bayesian practice, they place seemingly artificial restrictions on legal programs and questions, such as disallowing unbounded recursion and allowing only simple equality conditions. We prove it is possible to make trustworthy probabilistic languages for Bayesian practice by using functional programming theory to define them mathematically and prove them correct. The specifications interpret programs using measure-theoretic probability, which is a complete enough theory of probability that we do not need to restrict programs or conditions. We demonstrate that these trustworthy languages are useful by implementing them, and using them to model and answer questions about typical probabilistic processes. We also model and answer questions about processes that are either difficult or impossible to reason about precisely using typical Bayesian mathematical tools.

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<p dir="ltr">Previous wok has established that multiple academic and cognitive skills can contribute to difficulty with mathematics (Bull & Lee, 2014; Morgan et al., 2019; Purpura Day et al., 2017; Schmitt et al., 2017). However, little is known about how using both domain-specific (i.e., numeracy) and domain-general skills (i.e., executive function (EF), language, vocabulary) can help to identify children at risk for mathematics difficulties. Given that an estimated 3% to 8% of children are diagnosed with a math related disability (Desoete et al., 2004) and even more children experience difficulties with mathematics, and that mathematics is an important predictor of academic and career success (Duncan et al., 2007; Watts, 2020) it is imperative to understand how both domain-specific and domain-general skills, along with key demographic factors, can be used to identify children at risk for future mathematics difficulties. <a href="" target="_blank">The current study utilized data from a longitudinal project that assessed children’s academic and cognitive skills over four time points: the fall and spring of preschool and kindergarten</a> in a state in the Midwest of the United States.The analytic sample for this study consisted of 674 children from three cohorts. <a href="" target="_blank">A person-centered latent profile analysis was used to generate profiles of early math learners using children’s early numeracy, math language, executive function (EF), literacy, and vocabulary skills. Based on the model fit statistics and interpretability, a six-profile solution emerged from the data.</a> The latent profile approach was compared to a variable-centered regression for identifying risk for mathematics difficulties. <a href="" target="_blank">Results</a> show that there is variability in performance profiles in a sample at the lower end of mathematics performance. This study <a href="" target="_blank">suggests that domain-general skills such as EF, literacy, and mathematical language skills can help to distinguish between different performance profiles of mathematics learners</a>. <a href="" target="_blank">Results also demonstrate that person-centered and variable-centered approaches should be used in conjunction with one-another to best identify children at risk for mathematics difficulties.</a></p>

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