Abstract. The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper we study this problem for finite state machines with inputs and outputs, and in particular for Moore machines. We develop three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of input-output traces into an incomplete Moore machine and then completes the machine with self-loops; (2) the PRPNI algorithm, which uses the well-known RPNI algorithm for automata learning to learn a product of automata encoding a Moore machine; and (3) the MooreMI algorithm, which directly learns a Moore machine using PTAP extended with state merging. We prove that MooreMI has the fundamental identification in the limit property. We also compare the algorithms experimentally in terms of the size of the learned machine and several notions of accuracy, introduced in this paper. Finally, we compare with OSTIA, an algorithm that learns a more general class of transducers, and find that OSTIA generally does not learn a Moore machine, even when fed with a characteristic sample.
The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper we study this problem for finite state machines with inputs and outputs, and in particular for Moore machines. We develop three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of input-output traces into an incomplete Moore machine and then completes the machine with self-loops; (2) the PRPNI algorithm, which uses the well-known RPNI algorithm for automata learning to learn a product of automata encoding a Moore machine; and (3) the MooreMI algorithm, which directly learns a Moore machine using PTAP extended with state merging. We prove that MooreMI has the fundamental identification in the limit property. We also compare the algorithms experimentally in terms of the size of the learned machine and several notions of accuracy, introduced in this paper. Finally, we compare with OSTIA, an algorithm that learns a more general class of transducers, and find that OSTIA generally does not learn a Moore machine, even when fed with a characteristic sample. arXiv:1605.07805v2 [cs.FL] 2 Sep 2016research on grammatical inference [15] which has studied similar, but not exactly the same problems, such as learning deterministic finite automata (DFA), which are special cases of Moore machines with a binary output, or subsequential transducers, which are more general than Moore machines.Our contributions are the following:1. We define formally the LMoMIO problem (learning Moore machines from input-output traces). Apart from the correctness criterion of consistency (that the learned machine be consistent with the given traces) we also introduce several performance criteria including size and accuracy of the learned machine, and computational complexity of the learning algorithm. 2. We adapt the notion of characteristic sample, which is known for DFA [15], to the case of Moore machines.Intuitively, a characteristic sample of a machine M is a set of traces which contains enough information to "reconstruct" M . The characteristic sample requirement (CSR) states that, when given as input a characteristic sample, the learning algorithm must produce a machine equivalent to the one that produced the sample. CSR is important, as it ensures identification in the limit: this is a key concept in automata learning theory which ensures that the learning algorithm will eventually learn the right machine when provided with a sufficiently large set of examples [18]. 3. We develop three algorithms to solve the LMoMIO problem, and analyze them in terms of computational complexity and other properties. We show that although all three algorithms guarantee consistency, only the most advanced among them, called MooreMI, satisfies the characteristic sample requirement. We also show that MooreMI achieves identification in the limit. 4. We report on a prototype implementation of all three algorithms and experimental results. The experiments show that Moor...
Manufacturers of automated systems and their components have been allocating an enormous amount of time and effort in R&D activities, which led to the availability of prototypes demonstrating new capabilities as well as the introduction of such systems to the market within different domains. Manufacturers need to make sure that the systems function in the intended way and according to specifications. This is not a trivial task as system complexity rises dramatically the more integrated and interconnected these systems become with the addition of automated functionality and features to them. This effort translates into an overhead on the V&V (verification and validation) process making it time-consuming and costly. In this paper, we present VALU3S, an ECSEL JU (joint undertaking) project that aims to evaluate the state-of-the-art V&V methods and tools, and design a multi-domain framework to create a clear structure around the components and elements needed to conduct the V&V process. The main expected benefit of the framework is to reduce time and cost needed to verify and validate automated systems with respect to safety, cyber-security, and privacy requirements. This is done through identification and classification of evaluation methods, tools, environments and concepts for V&V of automated systems with respect to the mentioned requirements. VALU3S will provide guidelines to the V&V community including engineers and researchers on how the V&V of automated systems could be improved considering the cost, time and effort of conducting V&V processes. To this end, VALU3S brings together a consortium with partners from 10 different countries, amounting to a mix of 25 industrial partners, 6 leading research institutes, and 10 universities to reach the project goal.
This paper pilots Schulz generalised matrix inverse algorithm as a paradigm in demonstrating how computer aided reachability analysis and theoretical numerical analysis can be combined effectively in developing verification methodologies and tools for matrix iterative solvers. It is illustrated how algorithmic convergence to computed solutions with required accuracy is mathematically quantified and used within computer aided reachability analysis tools to formally verify convergence over predefined sets of multiple problem data. In addition, some numerical analysis results are used to form computational reliability monitors to escort the algorithm on-line and monitor the numerical performance, accuracy and stability of the entire computational process. For making the paper self-contained, formal verification preliminaries and background on tools and approaches are reported together with the detailed numerical analysis in basic mathematical language. For demonstration purposes, a custom made reachability analysis program based on affine arithmetic is applied to numerical examples.
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