Verified Quadratic Virtual Substitution for Real Arithmetic

Lecture Notes on Virtual Substitution & Real Arithmetic

Reasoning about cyber-physical systems and hybrid systems requires understanding and handling their real arithmetic, which can be challenging, because cyber-physical systems can have complex behavior. Differential dynamic logic and its proof calculus [Pla08, Pla10, Pla12] reduce the verification of hybrid systems to real arithmetic. How arithmetic interfaces with proofs has already been discuss...

From Heyting's arithmetic to verified programs

Essential Incompleteness of Arithmetic Verified by Coq

A constructive proof of the Gödel-Rosser incompleteness theorem [9] has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive functions are proved to be representable in a weak axiom system. Formulas and proofs are encoded as natural n...

Arithmetic of Quadratic Forms

has a solution in Fn. The representation problem of quadratic forms is to determine, in an effective manner, the set of elements of F that are represented by a particular quadratic form over F . We shall discuss the case when F is a field of arithmetic interest, for instance, the field of complex numbers C, the field of real numbers R, a finite field F, and the field of rational numbers Q. The ...

Navigation Using Sensory Substitution in Real and Virtual Mazes

Under certain specific conditions people who are blind have a perception of space that is equivalent to that of sighted individuals. However, in most cases their spatial perception is impaired. Is this simply due to their current lack of access to visual information or does the lack of visual information throughout development prevent the proper integration of the neural systems underlying spat...