A practical introduction to active automata learning

Transcription

1 A practical introduction to active automata learning Bernhard Steffen, Falk Howar, Maik Merten TU Dortmund SFM2011 Maik Merten, learning technology 1

2 Overview Motivation Introduction to active automata learning Practical aspects in active automata learning Conclusions

3 Mealy machines Mealy machine M=(S,,,, ) S finite set of states finite input-alphabet finite output-alphabet : (S x ) S transition-function : (S x ) output-function Words * for (s S, a, w *) :(S x *) S, (s, )=s, (s,aw) = ( (s,a),w) : (S x *) *, (s, )=, (s,aw) = (s,a). ( (s,a),w)

4 Active automata learning a L? MQ-Oracle Σ={a,b} no b b a a a a b b Learner no, bb L! a a,b b? EQ-Oracle

5 Angluin's alg. for Mealy machines ε D a b distingushing set state cover set S Initialize Distinguishing Set D with alphabet of inputs a b one transition extensions SA

6 Angluin's alg. for Mealy machines ε a b 0 0 Unknown system: a b

7 Angluin's alg. for Mealy machines a b ε 0 0 Unclosure: Rows in lower part that are not in upper part a 1 1 b 1 1

8 Angluin's alg. for Mealy machines a b ε 0 0 a 1 1 Unclosure: Rows in lower part that are not in upper part b 1 1 aa 1 1 ab 1 1

9 Angluin's alg. for Mealy machines a b ε 0 0 a 1 1 b 1 1 aa 1 1 ab 1 1 Conjecture: Unique rows in S become states Rows in S and SA become transitions

10 Angluin's alg. for Mealy machines a b ε 0 0 a 1 1 Counterexample: bbb / 010 b 1 1 aa 1 1 ab 1 1

11 Angluin's alg. for Mealy machines a b ε 0 0 a 1 1 b 1 1 bb 0 0 bbb 0 0 aa 1 1 ab 1 1 ba 0 0 Counterexample: bbb / 010 Insert all prefixes of the counterexample to upper part Extend SA accordingly

12 Angluin's alg. for Mealy machines a b ε 0 0 a 1 1 b 1 1 bb 0 0 bbb 0 0 aa 1 1 ab 1 1 ba 0 0 Inconsistency: Equal rows in upper part have different extensions 00

13 Angluin's alg. for Mealy machines a b ε 0 0 a 1 1 b 1 1 bb 0 0 bbb 0 0 aa 1 1 ab 1 1 ba 0 0 Inconsistency: Equal rows in upper part have different extensions 00 00

14 Angluin's alg. for Mealy machines a b ε 0 0 a 1 1 b 1 1 bb 0 0 bbb 0 0 aa 1 1 ab 1 1 ba 0 0 Inconsistency: Equal rows in upper part have different extensions b and bbb differ, e.g., for suffix b => ε and bb will differ for suffix bb

15 Angluin's alg. for Mealy machines a b bb ε a b bb bbb aa ab ba Inconsistencies lead to new columns New Conjecture

16 Angluin's alg. for Mealy machines Target System Learned System

17 Summarized Observations (1) Systematic completition of the observation table New states arise as targets of transitions or from counter examples of the equivalence queries. Technically: prefixes are added to S Closure procedure extends SA Consistency is enforced by enlarging the Distinguishing Set D

18 Summarized Observations (2) Invariance Lemma: All hypothesis models are totally defined: each input is considered at each state, input deterministic: there is only one transition per input at each state, transition covered: each transition lies on a path of the original system, state minimal: two different states in a hypothesis model always have a separating future á la Nerode).

19 Myhill Nerode Nerode relation: For language L define relation R L (for u,u Σ*) u R L u for all v Σ*: (uv L uv L) Myhill-Nerode Theorem: Minimal number of states of an accepting deterministic automaton equals the number of equivalence classes of R L

20 Summarized Observations (4) This (Nerode s theorem) directly yields: Corollary: Hypothesis automata have at most as many states as the smallest deterministic equivalent automaton. We will denote the number of states by n.

21 Summarized Observations (4) Lemma: The number of states of the hypothesis model increases in response to a counterexample. Theorem: Angluin s algorithm terminates after at most n equivalence queries with the smallest deterministic system representing the behaviour of the system to be learned.

22 Further Developments 22

23 Practical challenges Interface description etc. interfacing real systems: - alphabet generation - abstraction - data equivalence queries Behavioral models <presence type= /> Available reset <iq type= result /> Test-driver membership queries OK

24 Learning setup in Practice <presence type= /> Available <iq type= result /> TestDriver Static Alphabet Abstraction OK LearnLib Bern hard

25 A cegar teacher <presence type= /> Available(type=avail ) <iq type= result /> TestDriver OK LearnLib Learning relative to a given Representation System Available Available(type=avail ) Available Available(type=unavail ) Non-det. during EQ Test Cegar teacher

26 Counter Examples and Witnesses c 1 c 2 c 3 c 4 c 5 c 6 γ(α(c 1 )) γ(α(c 2 )) γ(α(c 3 )) γ(α(c 4 )) γ(α(c 5 )) γ(α(c 6 )) Bern hard

27 Counter Examples and Witnesses c 5 c 6 γ(α(c 1 )) γ(α(c 2 )) γ(α(c 3 )) c 4 γ(α(c 4 )) c 5 c 6 Bern hard

28 Counter Examples and Witnesses c 5 c 6 c 4 γ(α(c 1 )) γ(α(c 2 )) γ(α(c 3 )) d p γ(α(c 4 )) c 5 c 6 Bern hard Separating Pattern p c 4 d state representation future

29 Alphabet Abstraction Refinement Σ C Σ C \ α old (c) c γ(α(p)) x d F γ(α(p)) c d F α old (c) γ old (α old (c)) Bernhard Steffen VMCAI Austin, Texas

30 Case Study Biometric Passport [Aarts et. al, 2010] 262 Concrete symbols, 256 x readfile(i). - 1 initial abstract symbols - 8 alphabet refinements, to split readfile - 9 final abstract symbols read file(i) aggregated according to the required Authentication Bern hard

31 Further Developments Learning Side-Effects 31

32 Register automata (RA) action with formal parameters - parallel assignment Register (X): x 1. username x 2. password - + guard

33 Experimental results

34 Overview Motivation Introduction to active automata learning Practical aspects in active automata learning Conclusions

35 Learning non-functional properties New test-driver architecture Allows learning of non-functional properties Bundling of queries allows application of performance testing methods Performance Reliability Latency

36 Non-functional properties: First results

37 Profiling example: creating conferences

38 Practical results I Learning the OCS 38

39 User model: paper workflow

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41 Hierarchy

42 Submit Report Event Condition Action

43 Semantics of "phase expires"- edges (2)

44 Many participants

45 Putting it all together ocs Jboss DB Tomcat JEE JMS ECA Workflows

46 Regular extrapolation

47 Optimized learning setup

48 Conclusions Active Automata Learning in practice: has many facets: Abstraction Instrumentation Reuse/Optimization It establishes a new system perspective Systems as evolving beasts : to be observed continuously difficult to control with Functional and Non-Function Properties Behavioural perspective to control system evolution