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Graph algorithms exploiting minimization of boolean formula conjunctive normal form.

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The following two graph algorithm that exploit boolean formula minimization of conjunctive normal form (CNF) are implemented and hosted on GitHub Pages:

  • Determining prime implicant of a boolean function.
    If an adjacency matrix is created, namely the number of variables is equal to the number of clauses (the matrix is square) and every clause contains consecutive variable (sum with identity matrix, ie. ones on the main diagonal), minimal vertex stable sets are calculated with kernels highlighted in red, and a graph can be drawn.
  • Optimal graph vertex coloring; the graph is defined by its binary incidence matrix.

The prime implicant of the CNF is calculated with the exhaustive search approach, there is no Quine-McCluskey algorithm implemented.

Please be advised the user interface is in Polish, as the applications were designed to be teaching aid in classes taken in Polish language.

Tech stack (apps were created in 2014):

  • TypeScript
  • declarative bindings with Knockout.js
  • Bootstrap for responsive UI
  • jQuery
  • HTML5 / CSS3
  • Visual Studio 2013

Determining prime implicant
Graph vertex coloring