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Safety-critical software systems can only support a limited number of failures. Extensive testing is good at catching errors, however that will never certify their absence. Formal verification is an alternative to testing that can (automatically) provide a ...
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 ...
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
We present an algorithm for generating all polynomial invariants of P-solvable loops with assignments and nested conditionals. We prove termination of our algorithm. The proof relies on showing that the dimensions of the prime ideals from the minimal decom ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010
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
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 ...
We present a semi-decision procedure for checking satisfiability of formulas in the language of algebraic data types and integer linear arithmetic extended with user-defined terminating recursive functions. Our procedure is designed to integrate into a DPL ...
