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.
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.
@cite_27
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This paper introduces a framework for inference of timed temporal logic properties from data. The dataset is given as a finite set of pairs of finite-time system traces and labels, where the labels indicate whether the traces exhibit some desired behavior (e.g., a ship traveling along a safe route). We propose a decision-tree based approach for learning signal temporal logic classifiers. The method produces binary decision trees that represent the inferred formulae. Each node of the tree contains a test associated with the satisfaction of a simple formula, optimally tuned from a predefined finite set of primitives. Optimality is assessed using heuristic impurity measures, which capture how well the current primitive splits the data with respect to the traces' labels. We propose extensions of the usual impurity measures from machine learning literature to handle classification of system traces by leveraging upon the robustness degree concept. The proposed incremental construction procedure greatly improves the execution time and the accuracy compared to existing algorithms. We present two case studies that illustrate the usefulness and the computational advantages of the algorithms. The first is an anomaly detection problem in a maritime environment. The second is a fault detection problem in an automotive powertrain system. We consider the scenario where the executions of different business processes are traced into a log, where each trace describes a process instance as a sequence of low-level events representing basic kinds of operations. In this context, we address a novel problem: given a description of the processes' behaviors in terms of high-level activities instead of low-level events, and in the presence of uncertainty in the mapping between events and activities, find all the interpretations of each trace @math . Specifically, an interpretation is a pair @math that provides a two-level "explanation" for @math : @math is a sequence of activities that may have triggered the events in @math , and W is a process whose model admits @math . To solve this problem, we propose a probabilistic framework representing "consistent" @math 's interpretations, where each interpretation is associated with a probability score. The paper focuses on the problems of passive and active FSM inference as well as checking sequence generation. We consider the setting where an FSM cannot be reset so that its inference is constrained to a single trace either given a priori in a passive inference scenario or to be constructed in an active inference scenario or aiming at obtaining checking sequence for a given FSM. In each of the last two cases, the expected result is a trace representing a checking sequence for an inferred machine, if it was not given. We demonstrate that this can be achieved by a repetitive use of a procedure that infers an FSM from a given trace (identifying a minimal machine consistent with a trace) avoiding equivalent conjectures. We thus show that FSM inference and checking sequence construction are two sides of the same coin. Following an existing approach of constructing conjectures by SAT solving, we elaborate first such a procedure and then based on it the methods for obtaining checking sequence for a given FSM and inferring a machine from a black box. The novelty of our approach is that it does not use any state identification facilities. We demonstrate that the proposed approach can also be constrained to find a solution in a subset of FSMs represented by a nondeterministic mutation machine. Experiments with a prototype implementation of the developed approach using an existing SAT solver indicate that it scales for FSMs with up to a dozen of states and requires relatively short sequences to identify a black box machine. In this paper, we propose a mathematical framework to jointly model related activities with both motion and context information for activity recognition and anomaly detection. This is motivated from observations that activities related in space and time rarely occur independently and can serve as context for each other. The spatial and temporal distribution of different activities provides useful cues for the understanding of these activities. We denote the activities occurring with high frequencies in the database as normal activities. Given training data which contains labeled normal activities, our model aims to automatically capture frequent motion and context patterns for each activity class, as well as each pair of classes, from sets of predefined patterns during the learning process. Then, the learned model is used to generate globally optimum labels for activities in the testing videos. We show how to learn the model parameters via an unconstrained convex optimization problem and how to predict the correct labels for a testing instance consisting of multiple activities. The learned model and generated labels are used to detect anomalies whose motion and context patterns deviate from the learned patterns. We show promising results on the VIRAT Ground Dataset that demonstrates the benefit of joint modeling and recognition of activities in a wide-area scene and the effectiveness of the proposed method in anomaly detection.