Universal Decision Elements in 4-valued Logic

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Future Possibilities, Parallel Computing

The challenge of finding how many universal decision elements there are in four valued logic might be possible on a laptop after all: the program might reach a point where no UDEs with higher numbers of unused entry points are produced, and because of the number of lower-order UDEs that can now be processed, one might have confidence that the end of the road had indeed been reached.

But one could not be sure: maybe analysing more UDEs of lower unused EPs would have produced one capable of producing one with more than 32 unused EPs. Maybe some untried combination of values in a UDE would have produced a 32+. Perhaps only exhaustive processing, not possible on a laptop, could settle the matter. The problem would seem to lend itself perfectly to massively parallel processing.

A large number of UDEs can be examined in parallel. Each of these engines would generate new UDE/EP sets. A second process would check whether each new set is a duplicate of a set already generated. If not, a third process would check if the new UDE is a subset of a set already generated. If not, a fourth process would find if a new UDE is a superset of old sets and delete old subsets. A fifth process would take new UDEs that have made it through processes two and three and add them to the UDE master file.

The Fortran program logic page contains a summary of how the program has been enhanced and some of the techniques that now make it run so much faster.

Universal Decision Elements In Four Valued Logic

Webpages written: May 9th 2012 - December 2016 (on and off)
Copyright M Harding Roberts 2012 - 2016

Reference: A Method for Finding Formulae Corresponding to First Order Universal Decision Elements in m-Valued Logic by John Loader