Dictionary

complexity function en · NOUN

Meanings

1. (of a string) A function that counts the number of distinct factors (substrings of consecutive symbols) in a string of symbols;
   • It follows that #92;bullet The length function l#58;A#42;#92;longrightarrow#92;mathcalN is a complexity function on A#42;. 2002, A. V. Borovnik, A. G. Myasnikov, V. Shpilrain, “Measuring Sets in Infinite Groups”, in Robert H. Gilman, Alexei G. Myasnikov, Vladimir Shpilrain, editors, Computational and Statistical Group Theory, American Mathematical Society, page 27:
   • 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.
2. (of a formal language, of a string) 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. ▸ a function that counts the number of words of a given length.
3. (of an algorithm) A function representing the computational complexity an algorithm.
   • Hence, the worst case time complexity function of Floyd's algorithm is O(n³). 2014, R. Panneerselvam, Research Methodology, 2nd edition, PHI Learning, page 512:
   • 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). 2011, Richard Neapolitan, Kumarss Naimipour, Foundations of Algorithms, 4th edition, Jones & Bartlett Publishers, page 31:
   • 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.

Forms

Deriveds

volume complexity function · time complexity function · group complexity function · abelian complexity function

Translations (3)

de Komplexitätsfunktion (function that represents the computational complexity of an algorithm) · de Komplexitätsfunktion (function that counts distinct factors of a string) · de Komplexitätsfunktion (function that counts distinct words of a given length in a language)