# CAIA as a mathematician (Part 3)

All in all, the explanation given for CAIA’s solution of the Saint-Exupéry problem is very simple. It includes only two important choices: what disjunction for the backtrack, and what value for L. For all the other steps of its proof, CAIA uses a combinatorial method: it applies every of its mathematical rules that can be […]

# CAIA as a mathematician (Part 2)

Let us consider the beginning of the proof given in Diophante site. Three new unknowns appear, defined by: M/N=(C-A)/B=B/(C+A) the parities of M and N being different. This gives: A/(M2-N2)=B/(2*M*N)=C/(M2+N2)=D D is an integer because two denominators have never a common factor. Therefore, one has to solve: 2*M*N*(N-M)*(N+M)*D2=311850*P As either M or N is even, […]

# CAIA as a mathematician (Part 1)

It is interesting, to compare the solutions found by CAIA with those found by a human mathematician. Diophante is a very useful site, which proposes many mathematical problems, with one, and sometimes several, solution. I will consider the solution found by CAIA, and the one given by Diophante for the same problem. One finds it […]

# Bootstrapping CAIA Part III

For the realization of a General Problem Solving system, a number of meta-problems arise. The main idea of bootstrapping is that these meta-problems will be solved by the system itself, in the same way as it solves the problems for which it was designed. CAIA is quite an elaborate system; however, it is not yet […]

# Bootstrapping CAIA Part II: Choosing a new domain

There are many ways to increase the range of problems that CAIA could solve. For instance, one can introduce continuous variables, or define unknowns with an infinite number of possible values. It would also be interesting to consider meta-problems, that can be convenient to CAIA when it is solving a problem, for instance to monitor […]

# Bootstrapping CAIA Part I: The initial domain

I can’t just say “one must bootstrap AI”, how to do it must also be explained. Naturally, I will use my own experience in CAIA’s development, started in 1985. I shall quickly go through the first step, where I defined a language and knowledge for translating itself into C programs. This is well known by […]

# CAIA is not a good magician

Too often, IA researchers describe the successes of their system, but they keep a lower profile when they get poor outcomes. I do not want to comply to this bad habit. I describe here CAIA’s behavior when success does not come, in the present case, the magic square problem. An order N Magic Square has […]

# CAIA surprised me Part III The results

After finding symmetries, CAIA tries to find solutions to the magic cube problem, applying rules that enrich its formulation. One of these rules states that, when there is a bijection between a set of unknowns and a set of values, the sum of the unknowns equals the sum of the values. Therefore, CAIA adds the […]

# CAIA surprised me Part II The symmetries

For the cube problem described in the preceding post, CAIA begins with looking for symmetries in the problem formulation. What is a symmetry? For Richard Feynman: « A thing is symmetrical if there is something we can do to it so that after we have done it, it looks the same as it did before. » There […]

# CAIA surprised me Part I

An AI researcher can always arrange his system so that it can find a solution that he already knows. To do that, he chooses a formulation well adapted to this solution, he includes all the methods necessary for this solution, and he indicates to avoid the roads that do not lead to the right direction. […]