The goal of the Boticelli project is to show the usefulness of piecewise linear functions (PLFs) in various tasks of autonomous mobile robot navigation. One of the tasks is to deal with the world model where the 3D occupancy function is efficiently represented as a PLF; and the other is to represent the value function during reinforcement learning for the purpose of path planning. The paper overviews the project and demonstrates that the PLF approximation, as a solution to Bellman's equation, can support robot motion planning.

In this work reinforcement learning was successfully applied to several simulated control problems including pendulum swing-up, pole balancing and a difficult challenge that can roughly be described as balancing a basketball on one's finger. Compared to the first two tasks, the ball-balancing task is much harder. Control is achieved by using a piecewise linear approximant of the Q-function learned by an adaptive logic network (ALN) which solves Bellman's equation in a high-dimensional space.

A general study is made of two basic integrity constraints on relations: functional and multivalued dependencies. The latter are studied via an equivalent concept: decompositions. A model is constructed for any possible combination of functional dependencies and decompositions. The model embodies some decompositions as unions of relations having different schemata of functional dependencies. This suggests a new, stronger integrity constraint, the degenerate decomposition. More generally, the theory demonstrates the importance of using the union operation in database design and of allowing different schemata on the operands of a union. Techniques based on the union lead to a method for solving the problem of membership of a decomposition in the closure of a given set of functional dependencies and decompositions. The concept of antiroot is introduced as a tool for describing families of decompositions, and its fundamental importance for database design is indicated.

The automatic synthesis of Boolean switching functions by adaptive tree networks is discussed. The concept of heuristic responsibility, by means of which parts of a tree become specialized to certain subsets of input vectors, is explained. Applications to pattern recognition and optical character recognition (OCR) problems are described.