Formal verification of real-world software systems remains challenging for a number of reasons, including lack of automation, friction in specifying properties, and limited support for the diverse programming paradigms used in industry. In this thesis we m ...
We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rul ...
As of today, programming has never been so accessible. Yet, it remains a challenge for end-users: students, non-technical employees, experts in their domains outside of computer science, and so on. With its forecast potential for solving problems by only o ...
In this thesis, we explore techniques for the development and verification of programs in a high-level, expressive, and safe programming language. Our programs can express problems over unbounded domains and over recursive and mutable data structures. We p ...
Let R be a semilocal principal ideal domain. Two algebraic objects over R in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all completions of R and its fract ...
We present an approach to program repair and its application to programs with recursive functions over unbounded data types. Our approach formulates program repair in the framework of deductive synthesis that uses existing program structure as a hint to gu ...
Ahlswede et al. in the seminal paper [1] have shown that in data transfer over networks, processing the data at the nodes can significantly improve the throughput. As proved by Li et al. in [2], even with a simple type of operation, namely linear operation ...
A large part of software written today is reactive. In contrast to batch mode systems, a reactive program continuously adapts itself to new input which often requires a substantial amount of engineering. Traditionally, reactive programs are implemented in ...
This thesis explores the use of specifications for the construction of correct programs. We go beyond their standard use as run-time assertions, and present algorithms, techniques and implementations for the tasks of 1) program verification, 2) declarative ...
Automated synthesis of program fragments from specifications can make programs easier to write and easier to reason about. To integrate synthesis into programming languages, software synthesis algorithms should behave in a predictable way: they should succ ...
Affine-invariant properties are an abstract class of properties that generalize some central algebraic ones, such as linearity and low-degree-ness, that have been studied extensively in the context of property testing. Affine invariant properties consider ...
This thesis concerns optimal packing problems of tubes, or thick curves, where thickness is defined as follows. Three points on a closed space curve define a circle. Taking the infimum over all radii of pairwise-distinct point triples defines the thickness ...
In conventional programming languages like Java, the interface for accessing databases is often inelegant. Typically, an entire separate database query language must be embedded inside a conventional programming language for programmers to access the full ...
This work contains the study of the algebra called al-Badī‘ fī al-ḥisāb (literally : "the Wonderful on calculation"), written by the Persian mathematician Abu Bakr Muḥammad ibn al-Ḥusain al-Karaǧi (previously known as ...
We describe the new software package Aligator for automatically inferring polynomial loop invariants, The package combines algorithms from symbolic summation and polynomial algebra with computational logic, and is applicable to the rich class of P-solvable ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2008
We discuss interesting properties of a general technique for inferring polynomial invariants for a subfamily of imperative loops, called the P-solvable loops, with assignments only. The approach combines algorithmic combinatorics, polynomial algebra and co ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2008
This work is dedicated to developing algebraic methods for channel coding. Its goal is to show that in different contexts, namely single-antenna Rayleigh fading channels, coherent and non-coherent MIMO channels, algebraic techniques can provide useful tool ...
The first part of this thesis studies the problem of symmetry breaking in the context of simple mechanical systems with compact symmetry Lie group G. In this part we shall assume that the principal stratum of the G-action on the configuration space Q of a ...
