This site offers different possibilities to deal with Boolean matrices using the XBOOLE system. XBOOLE is an implementation to handle orthogonal ternary vector lists which are characterized by

  • an unlimited number of binary vectors (restricted only by the used memory space),
  • dynamic memory allocation,
  • a space concept (execution of calculations in more than one Boolean space with arbitrary dimensions).

A ternary matrix is the most important data type in XBOOLE. The elements of these matrices can only be equal to one of the symbols "0", "1" or "-". The rows can be of any order (ternary vector lists - TVL), or the order can be fixed (using the variable tuple VT).

XBOOLE can be used to solve problems related to problems of the binary Boolean Algebra, the Boolean Differential Calculus and includes also particular matrix operations. In this context you can solve

  • logical design problems (switching networks and machines) which include composition, analysis, optimization and calculation of test data,
  • problems in discrete mathematics, particularly the use of graphs and relations and their application,
  • problems of discrete signal and image operations.

Different problems characterized as highly complex and mostly NP-hard were already solved successfully. To this categories belong

  • the design of combinatorial switching networks using different algorithms and for different switching classes,
  • the simulation und qualitative analysis of digital circuits,
  • the calculation of test patterns for combinatorial switching networks,
  • the application of different graph and network models, their analysis and manipulation,
  • the analysis of one-dimensional (time- sensitive) and two-dimensional (discrete images) signal representations, e.g. for the recognition of layout structures.

To test the abilities of the XBOOLE system, you can choose two different ways on this site:

  • on the one hand you can use the application of the "XBOOLE Monitor";
  • on the other hand you can use the Java Applet "Distributed XBoole".

Usage information can be found under the menu item "information".


Logic Functions
Logic Functions and Equations
Binary Models for Computer Science
Posthoff, Christian, Steinbach, Bernd

Logikentwurf mit XBOOLE.
Verlag Technik, Berlin 1991
Bochmann, D.; Steinbach, B.