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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We illustrate the strength of Algebraic Methods, adapting GaussianElimination and Substitution to the problem of Exact Boolean Satisfiability.For 1-in-3 SAT with non-negated literals we are able to obtain considerablysmaller equivalent instances of 0/1 Integer Programming restricted to Equalityonly.  Both Gaussian Elimination and Substitution may be used in a processing step,followed by a type of brute-force approach on the kernel thus obtained.  Our method shows that Positive instances of 1-in-3 SAT may be reduced tosignificantly smaller instances of I.P.E. in the following sense. Any suchinstance of $|V|$ variables and $|C|$ clauses can be polynomial-time reduced toan instance of 0/1 Integer Programming with Equality, of size at most $2/3|V|$variables and at most $|C|$ clauses.  We obtain an upper bound for the complexity of counting, $O(2\kappa r2^{(1-\kappa) r})$ for number of variables $r$ and clauses to variables ratio$\kappa$.  We proceed to define formally the notion of a non-trivial kernel, definingthe problems considered as Constraint Satisfaction Problems.  We conclude showing the methods presented here, giving a non-trivial kernelfor positive 1-in-3 SAT, imply the existence of a non-trivial kernel for 1-in-3SAT.

Positive 1-in-3-SAT admits a non-trivial Kernel