What is the Final Year Project?

Pierce Convenience sampling dissertation Aaron Roth Citation: A correspondence between two different probabilistic programs or two runs of the same program Convenience sampling dissertation the specification of the c orrelation between corresponding pairs of random draws and then extending this coupling on samples to a coupling on the resulting output distributions, which can then be used to establish the desired property on the programs.

As Probabilistic Relation al Hoare Logic has just the right structure to be able to formally encode these coupling arguments, the thesis analyzes the structure of these arguments through this formal lens, justifying the attractiveness of the coupling approach in terms of compo sitionality.

It then considers an enriched logic and its connection to approximate couplings, which in turn are directly connected to differential privacy. Working in this logic, it gives novel proofs of some key constructions from differential priv acy, including the exponential and sparse vector mechanisms.

The proof for sparse vector is the first ever to be carried out in a machine-checkable form. Taken together, these results constitute a significant advance in our ability to mechanize key properties of important randomized algorithms such as those found in the differential privacy literature.

This thesis proposes abstractions and formal tools to develop correct LLVM peephole optimizations. A domain specific language DSL Alive enables the specification and verification of peephole optimizations. An Alive transformation is shown to be correct automatically by encoding the transformation and correctness criteria as constraints in first-order logic, which are automatically checked for validity using an SMT solver.

Peephole optimizations in LLVM are executed numerous times until no optimization is applicable and one optimization could undo the effect of the other resulting in non-terminating compilation.

A novel algorithm based on directed-acyclic-graph DAG composition determines whether such non-termination bugs can occur with a suite of peephole optimizations. The Alive toolkit can generate concrete input to demonstrate non-termination as well as automatically generating weakest preconditions.

It is actively used by the LLVM community and has detected numerous bugs in existing passes and is preventing bugs from being added to the compiler. Mike Gordon and Magnus Myreen Citation: This thesis establishes end-to-end verification with a comprehensive chain of connections all the way from the semantics of a theorem prover expressed in set theory down to x86 machine code running it.

It also makes striking use of self-application for both the compiler and the theorem prover. But more than that: Not only is this a compelling demonstration of the possibilities for formally correct software, and the promise of the CakeML system as an enabling technology for it, but gives perhaps the first really convincing correctness proof for the core of a higher-order logic interactive theorem prover.

It is possible that this combination of theorem prover and formally verified path to machine code will become one of the primary platforms for developing high-assurance software. This thesis proposes a new solution for the problem of concurrent program verification introducing the use of explicitly parallel models and logics to represent and reason about concurrent programs.

An effective way of finding a sweet spot in the cost-precision spectrum is provided, weaving together the two steps of constraint generation and cons traint resolution, offering a new way to think about proofs of concurrent programs.

Automated verification of imperative data structures such as lists is challenging because of the need to define complex loop invariants that have a sensible interpretation in an underlying program logic. This thesis presents a number of foundational results that greatly simplify the proof obligations that must be provided by the programmer for the verification of such programs.

Through the introduction and application of concepts such as deterministic transitive closure and property-directed reachability, the thesis demonstrates the feasibility of using a decidable logic EPR as an effective basis for answering reachability queries on an expressive class of imperative list-manipulating programs.

The thesis also extends these foundational ideas to define modular principles for reasoning about imperative data structures across procedure boundaries.

These contributions ultimately lead to a system that can effectively infer loop invariants from an expressive template family using existing SAT solver and shape analysis technology. Collectively, these results lead to a thesis that makes very important foundational and practical contributions to our understanding of the potential of automated program verification and its application to real-world programs.

The language and its accompanying metatheory introduce two important innovations. The first, and more technical, of these is the design of a core language combining a call-by-value evaluation order, a pragmatically motivated treatment of computational irrelevance to support compilation to efficient machine codeand a novel treatment of propositional equality.

This beautiful thesis will be a cornerstone of a new generation of language designs supporting significantly more robust and reliable software development.

Using software tools to explore the consequences of the design, derived directly from the mathematics, it showed that it has the desired behavior on many examples, and developed mechanized proofs that the design meets some of the original goals, showing that for programs in various subsets of the language one can reason in simpler models.

Third, the dissertation develops powerful theoretical foundations—based on logical relations and separation logic—for verifying the correctness of scalable concurrent algorithms via contextual refinement.

The members of the award committee were impressed with both the breadth and depth of the work, as well as the elegance of the exposition. It takes a type system — a highly scalable yet not quite precise method of dealing with programs — and refines it using Satisfiability Modulo Theory SMT techniques to compensate for the precision loss.Sampling: The Basics.

Sampling is an important component of any piece of research because of the significant impact that it can have on the quality of your results/findings. If you are new to sampling, there are a number of key terms and basic principles that act as a foundation to the subject.

This article explains these key terms and basic principles. Electrical Engineering and Computer Science (EECS) spans a spectrum of topics from (i) materials, devices, circuits, and processors through (ii) control, signal processing, and systems analysis to (iii) software, computation, computer systems, and networking.

Starbucks McKinsey 7S model is used to highlight the ways in which seven elements of businesses can be aligned to increase effectiveness.

According to this . T-Test. Hypothesis Testing and the Statistics T-Test. The t-test is probably the most commonly used Statistical Data Analysis procedure for hypothesis testing. Actually, there are several kinds of t-tests, but the most common is the "two-sample t-test" also known as the "Student's t-test" or the "independent samples t-test".

PROBABILITY AND NON-PROBABILITY SAMPLING:Convenience Sampling Research Methods Formal Sciences Statistics Business. Convenience sampling. Convenience sampling is a type of non-probability sampling technique.

Non-probability sampling focuses on sampling techniques that are based on the judgement of the researcher [see our article Non-probability sampling to learn more about non-probability sampling].

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Comparison of Convenience Sampling and Purposive Sampling :: Science Publishing Group