Re: Relation subset operators

On 7 juin, 01:09, Marshall <marshall.spi...@xxxxxxxxx> wrote:
On Jun 6, 2:19 pm, vadim...@xxxxxxxxx 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.
Marshall,

For what it's worth...

For having been involved in the exercice of attempting to build a
logical machine to be a sound evaluator for relational operations, I
have discovered that there is an intricate relationship between the
coherence of relation equation solving and the logical computing model
used to actually represent a single relation, given current
constraints imposed by memory/cpu architectures. In other words, the
two aspects simply can hardly be dissociated: building an relation
equation expressor without considering a serious work onto how there
are to be represented logically (and physically as a consequence) will
not only put such effort in jeopardy but will make one hit a stone
dead end due to the fact that a logical expression solvers built on
the principle of direct image systems relation representation, has a
very limited scope of verification.

I have designed a logical and computing model based on the principle
of representing relations thanks to fractal contructs which allows to
exploit other effective mathematical tools than traditional ra to
effectively operate relations and have the logical machine make
logical inferences as to the most appropriate formulation of a
relational operation. I am not sure that does make sense to somebody
who's involved deeply into the logical aspect of correctness but it is
a friendly word of warning.


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.
Yes it is but not without having a complete view of the problem and
taking into considerations the need for a sound logical representation
of relations.
Marshall

.

Relevant Pages

  • Re: Quantales, Dioids and Formal Language (was: Power Monoid)
    ... The structure that is a dioid is P, itself; not the generic monoid ... by the very natural of context-free and general ... The relation to the algebraic representation is that the mapping may ... the q's are regular expressions formed of context-free ...
    (sci.math.research)
  • Re: Exact (LISP-ish) calculations in Ruby?
    ... polynomials are definitely where it's easy -- I wrote something to ... messy library for handling mathematical expressions. ... messy object model to hold the expressions, ... reasonable representation. ...
    (comp.lang.ruby)
  • Re: Float comparison
    ... For example, when using IEEE 754 arithmetic, you perform ... apply a simple rounding algorithm that produces a real number that has ... a representation, and that is the representation of the result. ... mathematical expressions expressible in C yield rational numbers. ...
    (comp.lang.c)
  • Re: Relation subset operators
    ... The other curiosity is how many different RL expressions ... algebras is mega gigantic, and in algebras with operators that ... I added expression generator facility to QBQL. ... program and discover things than to write documentation! ...
    (comp.databases.theory)
  • Re: Relation subset operators
    ... Marshall (who is ... apparently in stealth mode) used to work on a program that generates ... The other curiosity is how many different RL expressions ... algebras is mega gigantic, and in algebras with operators that ...
    (comp.databases.theory)