English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present efficient algorithms to decide whether two given countingfunctions on non-abelian free groups or monoids are at bounded distance fromeach other and to decide whether two given counting quasimorphisms onnon-abelian free groups are cohomologous. We work in the multi-tape Turingmachine model with non-constant time arithmetic operations. In the case ofinteger coefficients we construct an algorithm of linear space and timecomplexity (assuming that the rank is at least $3$ in the monoid case). In thecase of rational coefficients we prove that the time complexity is $O(N\logN)$, where $N$ denotes the size of the input, i.e. it is as fast as addition ofrational numbers (implemented using the Harvey--van der Hoeven algorithm forinteger multiplication). These algorithms are based on our previous work whichcharacterizes bounded counting functions.

Efficient computations with counting functions on free groups and free monoids