19 citations · 34 across the 5 of their papers we have counts for
5 papers
Is Complexity a Source of Incompleteness?
Cristian S. Calude, Helmut Juergensen
In this paper we prove Chaitin's ``heuristic principle'', {\it the theorems of a finitely-specified theory cannot be significantly more complex than the theory itself}, for an appr…
From Heisenberg to Goedel via Chaitin
C. S. Calude, M. A. Stay
In 1927 Heisenberg discovered that the ``more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa''. Four years later Göd…
Transcending the Limits of Turing Computability
Vadim A. Adamyan, Cristian S. Calude, Boris S. Pavlov
Hypercomputation or super-Turing computation is a ``computation'' that transcends the limit imposed by Turing's model of computability. The field still faces some basic questions,…
Passages of Proof
Cristian S. Calude, Elena Calude, Solomon Marcus
In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragm…
Randomness Relative to Cantor Expansions
Cristian S. Calude, Ludwig Staiger, Karl Svozil
Imagine a sequence in which the first letter comes from a binary alphabet, the second letter can be chosen on an alphabet with 10 elements, the third letter can be chosen on an alp…