The Bifurcation Interpreter: A Step Towards the Automatic Analysis of Dynamical Systems

The Bifurcation Interpreter is a computer program that autonomously explores the steady-state orbits of one-parameter families of periodically- driven oscillators. To report its findings, the Interpreter generates schematic diagrams and English text descriptions similar to those appearing in the science and engineering research literature. Given a system of equations as input, the Interpreter uses symbolic algebra to automatically generate numerical procedures that simulate the system. The Interpreter incorporates knowledge about dynamical systems theory, which it uses to guide the simulations, to interpret the results, and to minimize the effects of numerical error.

Automatic Design of a Maglev Controller in State Space

We describe the automatic synthesis of a global nonlinear controller for stabilizing a magnetic levitation system. The synthesized control system can stabilize the maglev vehicle with large initial displacements from an equilibrium, and possesses a much larger operating region than the classical linear feedback design for the same system. The controller is automatically synthesized by a suite of computational tools. This work demonstrates that the difficult control synthesis task can be automated, using programs that actively exploit knowledge of nonlinear dynamics and state space and combine powerful numerical and symbolic computations with spatial-reasoning techniques.

Automatic Qualitative Modeling of Dynamic Physical Systems

This report describes MM, a computer program that can model a variety of mechanical and fluid systems. Given a system's structure and qualitative behavior, MM searches for models using an energy-based modeling framework. MM uses general facts about physical systems to relate behavioral and model properties. These facts enable a more focussed search for models than would be obtained by mere comparison of desired and predicted behaviors. When these facts do not apply, MM uses behavior-constrained qualitative simulation to verify candidate models efficiently. MM can also design experiments to distinguish among multiple candidate models.

Program Improvement by Automatic Redistribution of Intermediate Results

Introducing function sharing into designs allows eliminating costly structure by adapting existing structure to perform its function. This can eliminate many inefficiencies of reusing general componentssin specific contexts. "Redistribution of intermediate results'' focuses on instances where adaptation requires only addition/deletion of data flow and unused code removal. I show that this approach unifies and extends several well-known optimization classes. The system performs search and screening by deriving, using a novel explanation-based generalization technique, operational filtering predicates from input teleological information. The key advantage is to focus the system's effort on optimizations that are easier to prove safe.

TYPICAL: A Knowledge Representation System for Automated Discovery and Inference

TYPICAL is a package for describing and making automatic inferences about a broad class of SCHEME predicate functions. These functions, called types following popular usage, delineate classes of primitive SCHEME objects, composite data structures, and abstract descriptions. TYPICAL types are generated by an extensible combinator language from either existing types or primitive terminals. These generated types are located in a lattice of predicate subsumption which captures necessary entailment between types; if satisfaction of one type necessarily entail satisfaction of another, the first type is below the second in the lattice. The inferences make by TYPICAL computes the position of the new definition within the lattice and establishes it there. This information is then accessible to both later inferences and other programs (reasoning systems, code analyzers, etc) which may need the information for their own purposes. TYPICAL was developed as a representation language for the discovery program Cyrano; particular examples are given of TYPICAL's application in the Cyrano program.

Coherent Behavior from Incoherent Knowledge Sources in the Automatic Synthesis of Numerical Computer Programs

A fundamental problem in artificial intelligence is obtaining coherent behavior in rule-based problem solving systems. A good quantitative measure of coherence is time behavior; a system that never, in retrospect, applied a rule needlessly is certainly coherent; a system suffering from combinatorial blowup is certainly behaving incoherently. This report describes a rule-based problem solving system for automatically writing and improving numerical computer programs from specifications. The specifications are in terms of "constraints" among inputs and outputs. The system has solved program synthesis problems involving systems of equations, determining that methods of successive approximation converge, transforming recursion to iteration, and manipulating power series (using differing organizations, control structures, and argument-passing techniques).

The Design of a Mechanical Assembly System

This thesis describes a mechanical assembly system called LAMA (Language for Automatic Mechanical Assembly). The goal of the work was to create a mechanical assembly system that transforms a high-level description of an automatic assembly operation into a program or execution by a computer controlled manipulator. This system allows the initial description of the assembly to be in terms of the desired effects on the parts being assembled. Languages such as WAVE [Bolles & Paul] and MINI [Silver] fail to meet this goal by requiring the assembly operation to be described in terms of manipulator motions. This research concentrates on the spatial complexity of mechanical assembly operations. The assembly problem is seen as the problem of achieving a certain set of geometrical constraints between basic objects while avoiding unwanted collisions. The thesis explores how these two facets, desired constraints and unwanted collisions, affect the primitive operations of the domain.

Automatic Analysis of the Logical Structure of Programs

This report presents a method for viewing complex programs as built up out of simpler ones. The central idea is that typical programs are built up in a small number of stereotyped ways. The method is designed to make it easier for an automatic system to work with programs. It focuses on how the primitive operations performed by a program are combined together in order to produce the actions of the program as a whole. It does not address the issue of how complex data structures are built up from simpler ones, nor the relationships between data structures and the operations performed on them.

A Multiple-Context Equality-Based Reasoning System

Expert systems are too slow. This work attacks that problem by speeding up a useful system component that remembers facts and tracks down simple consequences. The redesigned component can assimilate new facts more quickly because it uses a compact, grammar-based internal representation to deal with whole classes of equivalent expressions at once. It can support faster hypothetical reasoning because it remembers the consequences of several assumption sets at once. The new design is targeted for situations in which many of the stored facts are equalities. The deductive machinery considered here supplements stored premises with simple new conclusions. The stored premises include permanently asserted facts and temporarily adopted assumptions. The new conclusions are derived by substituting equals for equals and using the properties of the logical connectives AND, Or, and NOT. The deductive system provides supporting premises for its derived conclusions. Reasoning that involves quantifiers is beyond the scope of its limited and automatic operation. The expert system of which the reasoning system is a component is expected to be responsible for overall control of reasoning.

ONTIC: A Knowledge Representation System for Mathematics

Ontic is an interactive system for developing and verifying mathematics. Ontic's verification mechanism is capable of automatically finding and applying information from a library containing hundreds of mathematical facts. Starting with only the axioms of Zermelo-Fraenkel set theory, the Ontic system has been used to build a data base of definitions and lemmas leading to a proof of the Stone representation theorem for Boolean lattices. The Ontic system has been used to explore issues in knowledge representation, automated deduction, and the automatic use of large data bases.

KAM: Automatic Planning and Interpretation of Numerical Experiments Using Geometrical Methods

KAM is a computer program that can automatically plan, monitor, and interpret numerical experiments with Hamiltonian systems with two degrees of freedom. The program has recently helped solve an open problem in hydrodynamics. Unlike other approaches to qualitative reasoning about physical system dynamics, KAM embodies a significant amount of knowledge about nonlinear dynamics. KAM's ability to control numerical experiments arises from the fact that it not only produces pictures for us to see, but also looks at (sic---in its mind's eye) the pictures it draws to guide its own actions. KAM is organized in three semantic levels: orbit recognition, phase space searching, and parameter space searching. Within each level spatial properties and relationships that are not explicitly represented in the initial representation are extracted by applying three operations ---(1) aggregation, (2) partition, and (3) classification--- iteratively.