Ordinary differential equations (ODEs) are ubiquitous when modeling continuous dynamics.
Classical numerical methods compute approximations of the solution, however without any …

Sturm's theorem is a well-known result in real algebraic geometry that provides a function
that computes the number of roots of a univariate polynomial in a semi-open interval, not …

A quantum circuit is a computational unit that transforms an input quantum state to an output
state. A natural way to reason about its behavior is to compute explicitly the unitary matrix …

Optical systems are becoming increasingly important by resolving many bottlenecks in
today's communication, electronics, and biomedical systems. However, given the continuous …

Due to major breakthroughs in software and engineering technologies, embedded systems
are increasingly being utilized in areas ranging from aerospace and next-generation …

Semilinear maps are a generalization of linear maps between vector spaces where we allow
the scalar action to be twisted by a ring homomorphism such as complex conjugation. In …

Complex vector analysis is widely used to analyze continuous systems in many disciplines,
including physics and engineering. In this paper, we present a higher-order-logic …

In order to verify the functional correctness of quantum circuits or algorithms, a prominent
approach is to specify them as quantum programs and semi-automatically deduce them in a …

Quantum computers are promising to efficiently solve hard computational problems,
especially NP problems. In this paper, we propose to tackle the formal verification of …

During the last decade, formal methods, in particular theorem proving, have proven to be
effective as analysis tools in different fields. Among them, quantum optics is a potential area …