Re: Relation subset operators

On Jun 6, 4:09 pm, Marshall <marshall.spi..._at_gmail.com> wrote:
> On Jun 6, 2:19 pm, vadim..._at_gmail.com wrote:
>
>
>
> > I'm still not sure if there are shorter versions. Marshall (who is
> > apparently in stealth mode) used to work on a program that generates
> > all valid RL expressions, and this looks like a problem fitted for
> > such a tool. The other curiosity is how many different RL expressions
> > one can generate with inversions and complements alone. For example,
> > the identities
>
> Yes, these are both things my program can handle. The theoretical
> aspects are fairly far along; what is killing me is the practical
> aspects.
> Namely, the number of possible expressions in even mildly complex
> algebras is mega gigantic, and in algebras with operators that
> are both commutative and associative, simply noting that two
> complex terms of the same size are syntactically equivalent
> is excruciatingly slow. I have recently purchased a much
> more powerful machine but I'm not sure how much this will
> help; the big wins have all been the results of greater
> understanding of the nature of Universal Algebra.
>
> I still have good ideas left for how to do better, and I
> believe a complete equational theory of Vadim's algebra
> is mechanically achievable.

I added expression generator facility to QBQL. The key to combinatorial explosion is to do a targeted search, rather than be overwhelmed by finding everything. The facility is not mature yet to search for relational division, but the search for x`` discovered the following amaizing identity:

x`` = ( x v R11 ) ^ ( x v R00 ).

P.S. I realize that until I write a decent tutorial and make a friendly user interface not many people (and most likely nobody at all) would bother checking up QBQL. However, it is so much fun to program and discover things than to write documentation! Received on Sat Jun 13 2009 - 21:22:23 CEST