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Integer NFB Factorization

No-factor-base (NFB) factorization of integer *n* amends Dixon's algorithm by searching common factors of the quadratic residues
modulo *n* using GCD. As a result, no optimization by the size of the factor base is necessary and
the heuristically measured computational complexity of the algorithm improves to

In number theory, integer factorization is the decomposition of a composite number into the product of primes. This is a challenging math problem and an interesting subject domain for application of Machine Understanding.

FORTH Machine

This FORTH interpreter with API to C/C++ was developed in the project of training combinatorial AI to use a Turing-complete language for programming. There were two ideas under this choice:

- postfix notation for algebraic expressions, which seems natural for AI, which is free from the common sense patterns of humans
- simple syntax for definition of new words, which commonly leads to bottom-to-top programming style - the thing that correlates with the approach of training combinatorial AI from simple to complex

Forth is a simple, yet extensible language and environment originally designed by Charles Moore. Forth features structured programming, reflection (as the ability to examine and modify program structure during execution), concatenative programming and extensibility (the programmer can create new commands). The modularity and extensibility of Forth permit writing significant programs.

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