As the development of formal proofs is a time-consuming task, it is important to devise ways
of sharing the already written proofs to prevent wasting time redoing them. One of the …

In this paper, I present a formalisation of a large portion of Apostol's Introduction to Analytic
Number Theory in Isabelle/HOL. Of the 14 chapters in the book, the content of 9 has been …

As the development of formal proofs is a time-consuming task, it is important to devise ways
of sharing the already written proofs to prevent wasting time redoing them. One of the …

In this paper, we discuss the formalization of the well known Gap Theorem of Complexity
Theory, asserting the existence of arbitrarily large gaps between complexity classes. The …

Reverse Complexity is a long term research program aiming at discovering the abstract,
logical principles underlying Complexity Theory, by means of a formal, reverse analysis of its …

ABSTRACT" A mathematician, like a painter or a poet, is a pattern maker. If his patterns are
more permanent than theirs, it is because they are made with ideas." GH Hardy Goldbach …

Οι αλγόριθμοι αποτελούν κύριο και ουσιώδες κομμάτι της διαδικαστικής γνώσης στα
Μαθηματικά. Μάλιστα, τα Μαθηματικά, υπό μία διασταλτική έννοια, είναι μόνο αλγόριθμοι. Ως …

Blum's speedup theorem is a major theorem in computational complexity, showing the
existence of computable functions for which no optimal program can exist: for any speedup …