Abstract. We consider various extensions and modifications of Shannon's General Purpose Analog Computer, which is a model of computation by differential equations in continuou...
Programs and Abstract Complexity A. Beckmann University of Wales Swansea Swansea, UK Axiom systems are ubiquitous in mathematical logic, one famous and well studied example being ï...
The Jordan Curve Theorem (JCT) states that a simple closed curve divides the plane into exactly two connected regions. We formalize and prove the theorem in the context of grid gr...
For a given positive integer k, sr(m, k) denotes the minimal positive integer such that every coloring of [n], n ≥ sr(m, k), that uses each color at most k times, yields a rainb...
: Taking as a starting point (a modification of) a weak theory of arithmetic of Jan Johannsen and Chris Pollett (connected with the hierarchy of counting functions), we introduce s...