Interactive theorem provers have been used extensively to reason about various software hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will lead to a successful proof requires a significant amount of human intervention. This paper presents an automated technique that takes as input examples of successful proofs and infers an Extended Finite State Machine as output. This can in turn be used to generate proofs of new conjectures. Our preliminary experiments show that the inferred models are generally accurate (contain few false-positive sequences) and that representing existing proofs in such a way can be very useful when guiding new ones.
@cite_27: From the Publisher: Classifier systems play a major role in machine learning and knowledge-based systems, and Ross Quinlan's work on ID3 and C4.5 is widely acknowledged to have made some of the most significant contributions to their development. This book is a complete guide to the C4.5 system as implemented in C for the UNIX environment. It contains a comprehensive guide to the system's use , the source code (about 8,800 lines), and implementation notes. The source code and sample datasets are also available on a 3.5-inch floppy diskette for a Sun workstation. C4.5 starts with large sets of cases belonging to known classes. The cases, described by any mixture of nominal and numeric properties, are scrutinized for patterns that allow the classes to be reliably discriminated. These patterns are then expressed as models, in the form of decision trees or sets of if-then rules, that can be used to classify new cases, with emphasis on making the models understandable as well as accurate. The system has been applied successfully to tasks involving tens of thousands of cases described by hundreds of properties. The book starts from simple core learning methods and shows how they can be elaborated and extended to deal with typical problems such as missing data and over hitting. Advantages and disadvantages of the C4.5 approach are discussed and illustrated with several case studies. This book and software should be of interest to developers of classification-based intelligent systems and to students in machine learning and expert systems courses.
Given a set of traces (see Definition ), the approach first infers the guard conditions. For each symbol @math the trace is scanned, identifying every instance where @math is applied, the variable values @math at that instance, and the label of the subsequent step in the trace. This is used to construct a training set where, with the use of standard machine learning algorithms (e.g. decision tree learners like @cite_27 ), it is possible to construct a model that predicts from a given pair label and data configuration what the subsequent label will be. In terms of EFSMs, this gives us @math , and implies some constraints on the order in which particular configurations of labels and variables can occur.