The current chapter presents an overview about the current stage of the foundational
ontology GFO. GFO (General Formal Ontology). GFO is a foundational ontology integrating …

Despite the plausible necessity of topological protection for realizing scalable quantum
computers, the conceptual underpinnings of topological quantum logic gates had arguably …

Randomized algorithms are widely used for finding efficiently approximated solutions to
complex problems, for instance primality testing and for obtaining good average behavior …

Real complexity theory is a resource-bounded refinement of computable analysis and
provides a realistic notion of running time of computations over real numbers, sequences …

Minlog is an interactive system which implements proof-theoretic methods and applies them
to verification and program extraction. We give an overview of Minlog and demonstrate how …

We give a coinductive characterization of the set of continuous functions defined on a
compact real interval, and extract certified programs that construct and combine exact real …

With the rise of increasingly advanced reverse engineering technique, especially more
scalable symbolic execution tools, software obfuscation faces great challenges. Branch …

Based on a new coinductive characterization of continuous functions we extract certified
programs for exact real number computation from constructive proofs. The extracted …

The objective of this paper is to provide a theoretical foundation for program extraction from
inductive and coinductive proofs geared to practical applications. The novelties consist in …

We introduce the first proof system for layered arithmetic circuits over an arbitrary ring R that
is (possibly) non-commutative and (possibly) infinite, while only requiring black-box access …