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.
The subsequent task is to derive an underlying state transition model that obeys and incorporates these data guards. To achieve this EFSMInfer applies an augmented version of the standard FSM state merging algorithm (Lang's Blue-Fringe algorithm @cite_4 ). The set of traces is first arranged as a prefix tree @cite_9 , where traces with the same prefix also share the same path from the root. Subsequently, states in the tree are merged according to the likelihood that they represent the same state, based on the similarity of their outgoing paths.
@cite_9 @cite_4
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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. Inferring a minimal finite state machine (FSM) from a given set of traces is a fundamental problem in computer science. Although the problem is known to be NP-complete, it can be solved efficiently with SAT solvers when the given set of traces is relatively small. On the other hand, to infer an FSM equivalent to a machine which generates traces, the set of traces should be sufficiently representative and hence large. However, the existing SAT-based inference techniques do not scale well when the length and number of traces increase. In this paper, we propose a novel approach which processes lengthy traces incrementally. The experimental results indicate that it scales sufficiently well and time it takes grows slowly with the size of traces. Traces are everywhere from information systems that store their continuous executions, to any type of health care applications that record each patient's history. The transformation of a set of traces into a mathematical model that can be used for a formal reasoning is therefore of great value. The discovery of process models out of traces is an interesting problem that has received significant attention in the last years. This is a central problem in Process Mining, a novel area which tries to close the cycle between system design and validation, by resorting on methods for the automated discovery, analysis and extension of process models. In this work, algorithms for the derivation of a Petri net from a set of traces are presented. The methods are grounded on the theory of regions, which maps a model in the state-based domain (e.g., an automata) into a model in the event-based domain (e.g., a Petri net). When dealing with large examples, a direct application of the theory of regions will suffer from two problems: one is the state-explosion problem, i.e., the resources required by algorithms that work at the state-level are sometimes prohibitive. This paper introduces decomposition and projection techniques to alleviate the complexity of the region-based algorithms for Petri net discovery, thus extending its applicability to handle large inputs. A second problem is known as the overfitting problem for region-based approaches, which informally means that, in order to represent with high accuracy the trace set, the models obtained are often spaghetti-like. By focusing on special type of processes called conservative and for which an elegant theory and efficient algorithms can be devised, the techniques presented in this paper alleviate the overfitting problem and moreover incorporate structure into the models generated. Obtaining accurate hidden Markov model (HMM) state sequences is a research challenge to warrant good system performance in particle filter (PF) compensation for noisy speech recognition. Instead of using specific knowledge at the model and state levels which is hard to estimate, we pool model states into clusters as side information. Since each cluster encompasses more statistics when compared to the original HMM states, there is a higher possibility that the newly formed probability density function at the cluster level can cover the underlying speech variation to generate appropriate PF samples for feature compensation. Testing the proposed PF-based compensation scheme on the Aurora 2 connected digit recognition task, we achieve an error reduction of 12.15 from the best multi-condition trained models using this integrated PF-HMM framework to estimate the cluster-based HMM state sequence information.