Descriptive Simulation: Combining Symbolic and Numerical Methods in the Analysis of Chemical Reaction Mechanisms

The Kineticist's Workbench is a computer program currently under development whose purpose is to help chemists understand, analyze, and simplify complex chemical reaction mechanisms. This paper discusses one module of the program that numerically simulates mechanisms and constructs qualitative descriptions of the simulation results. These descriptions are given in terms that are meaningful to the working chemist (e.g., steady states, stable oscillations, and so on); and the descriptions (as well as the data structures used to construct them) are accessible as input to other programs.

Symbolic Integration

SIN and SOLDIER are heuristic programs in LISP which solve symbolic integration problems. SIN (Symbolic INtegrator) solves indefinite integration problems at the difficulty approaching those in the larger integral tables. SIN contains several more methods than are used in the previous symbolic integration program SAINT, and solves most of the problems attempted by SAINT in less than one second. SOLDIER (SOLution of Ordinary Differential Equations Routine) solves first order, first degree ordinary differential equations at the level of a good college sophomore and at an average of about five seconds per problem attempted. The differences in philosophy and operation between SAINT and SIN are described, and suggestions for extending the work presented are made.

Symbolic Mathematical Laboratory

A large computer program has been developed to aid applied mathematicians in the solution of problems in non-numerical analysis which involve tedious manipulations of mathematical expressions. The mathematician uses typed commands and a light pen to direct the computer in the application of mathematical transformations; the intermediate results are displayed in standard text-book format so that the system user can decide the next step in the problem solution. Three problems selected from the literature have been solved to illustrate the use of the system. A detailed analysis of the problems of input, transformation, and display of mathematical expressions is also presented.

Maygen: A Symbolic Debugger Generation System

With the development of high-level languages for new computer architectures comes the need for appropriate debugging tools as well. One method for meeting this need would be to develop, from scratch, a symbolic debugger with the introduction of each new language implementation for any given architecture. This, however, seems to require unnecessary duplication of effort among developers. This paper describes Maygen, a "debugger generation system," designed to efficiently provide the desired language-dependent and architecture-dependent debuggers. A prototype of the Maygen system has been implemented and is able to handle the semantically different languages of C and OPAL.

The Kineticist's Workbench: Combining Symbolic and Numerical Methods in the Simulation of Chemical Reaction Mechanisms

The Kineticist's Workbench is a program that simulates chemical reaction mechanisms by predicting, generating, and interpreting numerical data. Prior to simulation, it analyzes a given mechanism to predict that mechanism's behavior; it then simulates the mechanism numerically; and afterward, it interprets and summarizes the data it has generated. In performing these tasks, the Workbench uses a variety of techniques: graph- theoretic algorithms (for analyzing mechanisms), traditional numerical simulation methods, and algorithms that examine simulation results and reinterpret them in qualitative terms. The Workbench thus serves as a prototype for a new class of scientific computational tools---tools that provide symbiotic collaborations between qualitative and quantitative methods.