Computability and Complexity in Self-assembly

Computability and Complexity

ion Abstraktion Acceptance problem Akzeptanz-Problem Accepted akzeptiert Accepting state akzeptierender Zustand Ackermann function Ackermann-Funktion Algorithm Algorithmus Alphabet Alphabet Ambiguity problem Zweideutigkeitsproblem Amortized analysis amortisierte Analyse Application Anwendung Argument (Funktions-)Argument Automaton (endlicher) Automat Automaton language (L(M)) die Sprache eines ...

Honest Computability and Complexity

Computations manipulate representations of objects, most often strings of symbols taken from some finite alphabet, rather than the objects themselves. Numbers, for example, are usually denoted by sequences of decimal, or binary, or unary digits. In logic, one therefore distinguishes between numbers n, which reside in an ideal Platonic world, and numerals ⌜n⌝, their symbolic representation as (f...

Computability and Complexity

Computability, Algorithmic Randomness and Complexity

I think mathematical ability manifests itself in many different ways. In particular, mathematicians can be drawn to space and geometry, can have strong analytic intuition, can be drawn to formalism, they can be drawn to counting arguments, etc. There is definitely no unique type of mathematician. Maybe those mathematicians who are drawn to algorithmic thinking have found a home in computer scie...

Self-assembly, modularity, and physical complexity.

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus, to any given type of physical structure that can be divided into building blocks. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of...