44 2033180199
All submissions of the EM system will be redirected to Online Manuscript Submission System. Authors are requested to submit articles directly to Online Manuscript Submission System of respective journal.
Journal of Pure and Applied Mathematics

Sign up for email alert when new content gets added: Sign up

A polynomial solution for the 3-SAT problem

Author(s): Geraldine Reichard

In this paper, an algorithm is presented, solving the 3-SAT problem in a polynomial runtime of which implies P = NP.
The 3-SAT problem is about determining, whether or not a logical expression, consisting of clauses with up to 3 literals connected by OR-expressions, that are interconnected by AND-expressions, is satisfiable.
For the solution a new data structure, the 3-SAT graph, is introduced. It groups the clauses from a 3-SAT expression into coalitions, that contain all clauses with literals consisting of the same variables. The nodes of the graph represent the variables connecting the corresponding coalitions.
An algorithm R will be introduced, that identifies relations between clauses by transmitting markers, called upgrades, through the graph, making use of implications. The algorithm will start sequentially for every variable and create start upgrades, one for
the variables negated and one for its non-negated literals. It will be shown, that the start upgrades have to be within a specific clause pattern, called edge pattern, to mark a beginning or ending of an unsatisfiable sequence.
It will be proven, that if after several execution steps of algorithm R, two corresponding start upgrades circle, then the expression is unsatisfiable and if no upgrade steps are possible anymore and the algorithm did not return unsatisfiable, the expression is satisfiable.
The algorithm R is similar to already existing solutions solving 2-SAT polynomial, also making use of implications using a graph.


PDF
 
Google Scholar citation report
Citations : 7299

Journal of Pure and Applied Mathematics received 7299 citations as per Google Scholar report

Journal of Pure and Applied Mathematics peer review process verified at publons
pulsus-health-tech
Top