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Machine Learning for Dynamic Software Analysis: Potentials and Limits pp 3–49Cite as

Machine Learning for Software Analysis: Models, Methods, and Applications

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11026))

Abstract

Machine Learning (ML) is the discipline that studies methods for automatically inferring models from data. Machine learning has been successfully applied in many areas of software engineering including: behaviour extraction, testing and bug fixing. Many more applications are yet to be defined. Therefore, a better fundamental understanding of ML methods, their assumptions and guarantees can help to identify and adopt appropriate ML technology for new applications.

In this chapter, we present an introductory survey of ML applications in software engineering, classified in terms of the models they produce and the learning methods they use. We argue that the optimal choice of an ML method for a particular application should be guided by the type of models one seeks to infer. We describe some important principles of ML, give an overview of some key methods, and present examples of areas of software engineering benefiting from ML. We also discuss the open challenges for reaching the full potential of ML for software engineering and how ML can benefit from software engineering methods.

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Notes

  1. 1.

    Informally identification in the limit means that for any infinite sequence of observations \(o_1, o_2 , \ldots \) there exists some finite point n after which the function learned from the first n observations is longer changed by any later observations.

  2. 2.

    Note that in general A and B can be cartesian products of sets, e.g. \(A = A_1 \times \ldots \times A_n\).

  3. 3.

    Here, the relation \(f(x_i) \equiv y_i\) means that \(f(x_i)\) is very close to \(y_i\) for some suitable metric. Of course one such relation is the equality relation on B.

  4. 4.

    By data smoothing we mean any form of statistical averaging or filtering process, that can reduce the effects of noise. Data smoothing may be necessary even when a relational model is appropriate.

  5. 5.

    This is done in many approaches including linear regression models, polynomial approximation, Fourier methods, simple neural networks and deep learning.

  6. 6.

    A universal algebraic structure is a many-sorted first-order structure \(\langle A_i : i = 1 , \ldots , n; c_j : j = 1 , \ldots , m; f_k : k = 1 , \ldots , p, \rangle \) consisting of data sets \(A_i\), constants \(c_j \in A_{i_j}\), and functions \(f_k : A_{i_{k(1)}} \times \ldots \times A_{i_{k(n)}} \rightarrow A_{i_{k(n+1)}}\) but no relations. Thus a deterministic Moore automaton is a 3-sorted universal algebraic structure. See e.g. [45] or [44] for further details.

  7. 7.

    Here supervised learning is more obvious if we think in terms of regular languages rather than automata. Then we are inferring the language acceptance function \(L: {\varSigma }^* \rightarrow \{ 0, 1 \}\) from a finite set of instances. However, the two viewpoints are equivalent by Kleene’s Theorem.

  8. 8.

    This assumption amounts to little more than retaining, i.e. not throwing away, any observational data.

  9. 9.

    For algebraists, the important fact here is that \(T({\varSigma }^*, \textit{Observations})\) is the initial object in the appropriate category of automata and homorphisms, which is unique up to isomorphism. See [46] for details.

  10. 10.

    The fundamental principle of initiality for \(T({\varSigma }^*, \textit{Observations})\) says that such folding is always possible.

  11. 11.

    For active learning, counterfactual evidence may eventually emerge that destroys the loop hypothesis, but in passive learning this is not possible.

  12. 12.

    Merging is a little complicated to define graph theoretically, so we leave it to the reader as an exercise!

  13. 13.

    Then \(v_1\) is a prefix of \(v_2\) or vice versa.

  14. 14.

    Assuming that \(v_1 . \sigma , v_2 . \sigma \in \textit{Queries}\).

  15. 15.

    Notice here that is a partial function, i.e. \(\delta \) is not necessarily defined on all arguments.

  16. 16.

    In a lattice, \((A, \le )\) a maximum element exceeds all others while a maximal element is exceeded by none. Thus a maximum element must be unique, while a maximal element need not be.

  17. 17.

    We actually present a simple generalisation of L* to an arbitrary output alphabet \({\varOmega }\). This algorithm is termed L*Mealy and first appeared in [34] where it was applied to Mealy machines.

  18. 18.

    Minimum state size seems to be a natural result of many active learning algorithms for Moore automata. This seems to be due to the difficulty of distinguishing pairs of states without any concrete evidence.

  19. 19.

    In model construction, red prefixes are needed to represent states, while blue prefixes are needed for defining transitions. According to our definition, a prefix can be both red and blue, but this is not problematic.

  20. 20.

    What to do when the SUL is non-deterministic will be discussed later.

  21. 21.

    For the reader familiar with algebra, condition (i) corresponds to an algebraic closure condition on the red prefix set under the operation of appending an input \(\sigma \in {\varSigma }\) and modulo row equivalence. The closure condition (ii) corresponds to row equivalence being a congruence on the red prefix set with respect to the state transition function \(\delta \). Thus the red prefix set is able to provide a state set for a quotient automaton defined by the table T.

  22. 22.

    For example, the short-lex ordering < on \({\varSigma }^*\) is suitable. Here \({\overline{\sigma }} < {\overline{\sigma }}'\) if \(\vert {\overline{\sigma }} \vert < \vert {\overline{\sigma }}' \vert \). If \(\vert {\overline{\sigma }} \vert = \vert {\overline{\sigma }}' \vert = n\) then \({\overline{\sigma }} < {\overline{\sigma }}'\) if, and only if \({\overline{\sigma }} < {\overline{\sigma }}'\) in the lexicographical ordering on \({\varSigma }^n\).

  23. 23.

    Notice that it is necessary to use a multiset of observations, i.e. to repeat previous SUL experiments, in order to establish frequencies and probabilities. Thus the cost of learning a probabilistic automaton may be quite high in terms of the query count.

  24. 24.

    http://learnlib.de.

  25. 25.

    See https://www.connect-forever.eu.

  26. 26.

    In fact congruences and quotients are universal constructions throughout the whole of mathematics.

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Acknowledgments

We gratefully acknowledge financial support for this research from the following projects: EU ITEA 3 project 16032 Testomat, EU ECSEL project 692529-2 SafeCOP, Vinnova FFI project 2013-05608 VIRTUES, ERC Advanced Grant no. 291652 (ASAP), and the EPSRC EP/R013144/1 SAUSE project. We are also very thankful to the Schloss Dagstuhl for their support of the Dagstuhl Seminar 16172 and for the participant to this workshop for their insightful discussions.

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  1. The Open University, Milton Keynes, UK

    Amel Bennaceur

  2. KTH Royal Institute of Technology, Stockholm, Sweden

    Karl Meinke

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    Amel Bennaceur

  2. Technische Universität Darmstadt, Darmstadt, Germany

    Reiner Hähnle

  3. KTH Royal Institute of Technology, Stockholm, Sweden

    Karl Meinke

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Bennaceur, A., Meinke, K. (2018). Machine Learning for Software Analysis: Models, Methods, and Applications. In: Bennaceur, A., Hähnle, R., Meinke, K. (eds) Machine Learning for Dynamic Software Analysis: Potentials and Limits. Lecture Notes in Computer Science(), vol 11026. Springer, Cham. https://doi.org/10.1007/978-3-319-96562-8_1

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