A linearly computable measure of string complexity

A linearly computable measure of string complexity

We present a measure of string complexity, called I-complexity, computable in linear time and space. It counts the number of different substrings in a given string. The least complex strings are the runs of a single symbol, the most complex are the de Bruijn strings. Although the I-complexity of a string is not the length of any minimal description of the string, it satisfies many basic propert...

Complexity of Computable Models

A computable measure of nonclassicality for light

We propose the entanglement potential (EP) as a measure of nonclassicality for quantum states of a single-mode electromagnetic field. It is the amount of two-mode entanglement that can be generated from the field using linear optics, auxiliary classical states and ideal photodetectors. The EP detects nonclassicality, has a direct physical interpretation, and can be computed efficiently. These t...

Information Complexity Is Computable

The information complexity of a function f is the minimum amount of information Alice and Bob need to exchange to compute the function f . In this paper we provide an algorithm for approximating the information complexity of an arbitrary function f to within any additive error > 0, thus resolving an open question as to whether information complexity is computable. In the process, we give the fi...

The Complexity of Computable Categoricity

We show that the index set complexity of the computably categorical structures is Π1-complete, demonstrating that computable categoricity has no simple syntactic characterization. As a consequence of our proof, we exhibit, for every computable ordinal α, a computable structure that is computably categorical but not relatively ∆α-categorical.