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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we present an average-case efficient algorithm to resolve the problem of determining whether two Boolean functions in trace representation are identical. Firstly, we introduce a necessary and sufficient condition for null Boolean functions in trace representation, which can be viewed as a generalization of the well-known additive Hilbert90 theorem. Based on this condition, we propose an algorithmic method with preprocessing to address the original problem. The worst-case complexity of the algorithm is still exponential; its average-case performance, however, can be improved. We prove that the expected complexity of the refined procedure is O(n), if the coefficients of input functions are chosen i.i.d. according to the uniform distribution over F2n ; therefore, it performs well in practice. key words: average-case analysis, Boolean functions in polynomial form, trace representation, univariate representation

An Average-Case Efficient Algorithm on Testing the Identity of Boolean Functions in Trace Representation