Meaning of complexity function | Babel Free

Definitions

1. A function that counts the number of distinct factors (substrings of consecutive symbols) in a string of symbols;
2. A function that counts the number of distinct factors (substrings of consecutive symbols) in a string of symbols; (of a formal language) a function that counts the number of words of a given length.
3. a function that counts the number of words of a given length.
4. A function representing the computational complexity an algorithm.

Equivalents

Examples

“It follows that #92;bullet The length function l#58;A#42;#92;longrightarrow#92;mathcalN is a complexity function on A#42;.”

“2003, Julien Cassaigne, Constructing Infinite Words of Intermediate Complexity, Masami Ito, Masafumi Toyama (editors), Developments in Language Theory: 6th International Conference, 6th International Conference, DLT 2002, Revised Papers, Springer, LNCS 2450, page 173, We present two constructions of infinite words with a complexity function that grows faster than any polynomial, but slower than any exponential.”

“2003, Roberto Segala, Verification of Randomized Distributed Algorithms, Ed Brinksma, Holger Hermanns, Joost-Pieter Katoen (editors), Lectures on Formal Methods and Performance Analysis, Springer, LNCS 2090, page 253, Let ϕ be a complexity function.”

“A complexity function need not have a quadratic term to be in O(n²). It need only eventually lie beneath some pure quadratic function on a graph. Therefore, any logarithmic or linear complexity function is in O(n²).”

“Hence, the worst case time complexity function of Floyd's algorithm is O(n³).”

CEFR level