Bernhard Steffen, Falk Howar, Malte Isberner TU Dortmund /CMU. B. Steffen Summer School CPS
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1 Active Automata Learning: From DFA to Interface Programs and Beyond or From Languages to Program Executions or (more technically) The Power of Counterexample Analysis Bernhard Steffen, Falk Howar, Malte Isberner TU Dortmund /CMU B. Steffen Summer School CPS
2 Connect Scenario some service connector interrogate learn X try to use inform about new service and device learner CONNECT environment interrogate look for known models B. Steffen Summer School CPS
3 Data-Dependent Control Value-independent Data Dependencies B. Steffen Summer School CPS
4 How to Extend w. Data? Data is crucial for modeling Interface specifications relate data in input to data in subsequent output Communication protocols sequence numbers, identifiers,.. (External) Mapper-Based Data Treatment Explicit Data Modelling B. Steffen Summer School CPS
5 Outline Background Manual Treatment of Data Automated Alphabet Abstraction Refinement Modelling Data Explicitly Conclusions B. Steffen Summer School CPS
6 Computer/Telephony Integrated Systems LAN Switch Model-Generator Application-PCs ISDN Network Application- Server B. Steffen Summer School CPS
7 The Concrete Scenario Test Coordinator Rational Robot Hipermon Hipermon HTTP CSTA II/III PCM Application PCs HTTP Hipermon Hipermon PCM Application Server B. Steffen Summer School CPS
8 Means of Observation Hipermon Test Coordinator Hipermon ^ HTTP Rational Robot CSTA II/III PCM Application PCs HTTP Hipermon Hipermon PCM Application Server (small) learned models imposed major test suite optimizations B. Steffen Summer School CPS
9 Moderated, Regular Extrapolation l Extrapolation Hypothesis Building beyond known facts l Regular Extrapolation-Universe: Extended Finite Automata l Moderated The Extrapolation Process requires targeted interaction Neither Correct nor Complete! B. Steffen Summer School CPS
10 Models in our Scenario Abstract representation of the protocol-level behaviour. Abstraction typically concerns { invokeid = 58391, replace operation-value = 21 (cstaeventreport), {eventspecificinfo.....hookswitch symbolic names details l i no time stamps etc. {deviceid.dialingnumber = 500 hookswitchonhook= TRUE,... timestamp = } }}} {obsevent deviceid = A1 switchonhook,... }} B. Steffen Summer School CPS
11 Sketch of the Model Structure Models comprise state changes as well as UPN- and CSTA-Observations. Sys_Info obs_csta upnoffhook obs_csta obs_csta obs_csta Sys_Info { {deviceid = A1 hookswitchonhook,... }} device A1 display(line 1,...) LEDs: (1,on) (2,off) B. Steffen Summer School CPS
12 Transitions Reaching Words Active Automata Learning OT Distinguishing Futures Lower Hypothesis Automaton Unknown System Closeness & Consistency Validation B. Steffen Summer School CPS
13 Membership Queries OT 1 Abstract States Unknown System a 1 b 0 Not closed! Transition Relation B. Steffen Summer School CPS
14 Closure & Consistency OT 1 b 0 Unknown System a 1 ba 0 bb 0 a Closed & Consistent b a,b B. Steffen Summer School CPS
15 Equivalence Queries OT 1 b 0 a 1 Unknown System ab 1 a 1 a ba 0 bb 0 b a,b Counterexample: ab L B. Steffen Summer School CPS
16 Counter Example-Based Extension OT 1 b 0 a 1 ab 1 a Unknown System ba 0 bb 0 aa 0 aba 0 abb 1 b a,b Counterexample: ab L B. Steffen Summer School CPS
17 Closure & Consistency OT 1 b 0 a 1 ab 1 ba 0 bb 0 Not consistent: row ( ) = row (a), but row ( a) row (aa) Unknown System aa 0 aba 0 abb 1 New Column: a B. Steffen Summer School CPS
18 Next Iteration OT a 1 1 b 0 0 a 1 0 Unknown System ab 1 0 ba 0 0 bb 0 0 Closed & Consistent aa 0 0 aba 0 0 abb 1 0 B. Steffen Summer School CPS
19 Next Iteration OT a 1 1 b 0 0 a 1 0 ab 1 0 ba 0 0 bb 0 0 aa 0 0 aba 0 0 abb 1 0 b a a,b a Unknown System b Finished! B. Steffen Summer School CPS
20 Active automata learning: L* a Σ={a,b} b b a a a b b aba L? MQ-Oracle no a a,b b? no, bb L! EQ-Oracle B. Steffen Summer School CPS
21 Summary of L* algorithm L* infers Finite State Machine from queries: 1. Pose membership queries until saturation 2. Construct Hypothesis from obtained information 3. Pose equivalence query 4. if no look at counterexample and goto 1 5. else return Hypothesis end Has been used to learn large automata ( 100 kstates) Adapted for Mealy Machines [Niese et al. 2003] and for Interface Automata [Aarts et al. 2010] Efficient Tool: LearnLib [TUDortmund] B. Steffen Summer School CPS
22 Summary of L* algorithm L* infers Finite State Machine from queries: 1. Pose membership queries until saturation 2. Construct Hypothesis from obtained information 3. Pose equivalence query 4. if no look at counterexample and goto 1 5. else return Hypothesis end Has been used to learn large automata ( 100 kstates) Adapted for Mealy Machines [Niese et al. 2003] and for Interface Automata [Aarts et al. 2010] Efficient Tool: LearnLib [TUDortmund] B. Steffen Summer School CPS
23 Analysis of Counterexamples I one essential suffix All prefixes of counterexample a b bb ε 0 0 a 1 1 b 1 1 bb 0 0 bbb 0 0 aa 1 1 ab 1 1 ba 0 0 B. Steffen Summer School CPS
24 Analysis of Counterexamples I one essential suffix All prefixes of counterexample a b bb ε 0 0 a 1 1 b 1 1 bb 0 0 bbb 0 0 aa 1 1 ab 1 1 ba 0 0 Essential suffix B. Steffen Summer School CPS
25 Effect: Reduced Observation Table Rivest and Shapire: Analyze counterexample separately (not in the table) Only add one essential suffix (i.e., witness), as column label to the table Consequence: Guaranteed Consistency! Improved worst case complexity BUT: Hypothesis Automata are no longer guaranteed to be minimal! (cf. Pnueli / Mahler s criticism) B. Steffen Summer School CPS
26 Outline Background Manual Treatment of Data Automated Alphabet Abstraction Refinement Modelling Data Explicitly Conclusions B. Steffen Summer School CPS
27 Simple Stack finite capacity B. Steffen Summer School CPS
28 Mappers B. Steffen Summer School CPS
29 Learning the stack as a language push, pop L, L stack.push(1) stack.pop() true, false, null, 1 B. Steffen Summer School CPS
30 Introducing outputs: Mealy machines push, pop OK, NOK, null, 1 stack.push(1) stack.pop() true, false, null, 1 B. Steffen Summer School CPS
31 Introducing outputs: Mealy machines push1, push2, pop stack.push(1) Stack.push(2) stack.pop() OK, NOK, null, 1, 2 true, false, null, 1, 2 B. Steffen Summer School CPS
32 Outline Background Manual Treatment of Data Automated Alphabet Abstraction Refinement Modelling Data Explicitly Conclusions B. Steffen Summer School CPS
33 Automated Alphabet Abstraction Refinement Learning setup in Practice <presence type= /> Available <iq type= result /> Test-driver Static alphabet abstraction OK LearnLib B. Steffen Summer School CPS
34 Automated Alphabet Abstraction Refinement <presence type= /> Available(type=avail ) <iq type= result /> Test-driver OK LearnLib Learning relative to a given representation system Available Available(type=avail ) Available Available(type=unavail ) Non-det. during EQ Test CEGAR teacher <presence type= /> Available <iq type= result /> Test-driver Static alphabet abstraction OK LearnLib B. Steffen Summer School CPS
35 The Mod-k Stack finite set of outputs, e.g.: odd / even push, push, pop OK, NOK, null, odd, even stack.push(51); stack.push(2012); stack.pop() true, false, null, 51, 2012 B. Steffen Summer School CPS
36 The Mod-k Stack finite set of outputs, e.g.: odd / even push push pop / odd push push pop / even push, push, pop OK, NOK, null, odd, even stack.push(51); stack.push(2012); stack.pop() true, false, null, 51, 2012 B. Steffen Summer School CPS
37 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 B. Steffen Summer School CPS
38 Counter Examples and Witnesses c 1 c 2 c 3 c 4 c 5 c 6 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 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 B. Steffen Summer School CPS
39 Counter Examples and Witnesses c 5 c 6 γ(α(c 1 )) γ(α(c 2 )) γ(α(c 3 )) c 4 d p γ(α(c 4 )) c 5 c 6 Separating pattern p c 4 d state representation future B. Steffen Summer School CPS
40 Alphabet Abstraction Refinement Σ C Σ C \ α old (c) c push γ(α(p)) x d = γ(α(p)) c d α old (c) γ old (α old (c)) push B. Steffen Summer School CPS
41 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 Bernhard Steffen VMCAI Austin, Texas B. Steffen Summer School CPS
42 Outline Background Manual Treatment of Data Automated Alphabet Abstraction Refinement Modelling Data Explicitly Conclusions B. Steffen Summer School CPS
43 How to Extend with Data? Data is crucial for modeling Interface specifications relate data in input to data in subsequent output Communication protocols sequence numbers, identifiers,.. Extend automaton model Data parameters in actions State variables to remember parameter values How to extend the learning techniques? 43 B. Steffen Summer School CPS
44 Register Automata B. Steffen Summer School CPS
45 Relation: Data Languages B. Steffen Summer School CPS
46 The Impact of Register Automata Query: push(p 1 )/OK push(p 2 )/OK pop()/p 2 push(p)/ok, pop()/o(p), L, L stack.push(51); stack.push(2012); stack.pop() true, false, null, 51, 2012 B. Steffen Summer School CPS
47 A Data-Aware Nerode-Relation B. Steffen Summer School CPS
48 Reusing structure of L* B. Steffen Summer School CPS
49 Analysis of Counterexamples III Counterexample Analysis for inferring New locations New registers New transitions B. Steffen Summer School CPS
50 CE: New location B. Steffen Summer School CPS
51 CE: New location B. Steffen Summer School CPS
52 CE: New location B. Steffen Summer School CPS
53 CE: New location B. Steffen Summer School CPS
54 CE: New location B. Steffen Summer School CPS
55 CE: New location B. Steffen Summer School CPS
56 CE: New register B. Steffen Summer School CPS
57 CE: New register B. Steffen Summer School CPS
58 CE: New register B. Steffen Summer School CPS
59 CE: New register B. Steffen Summer School CPS
60 CE: New transition B. Steffen Summer School CPS
61 CE: New transition B. Steffen Summer School CPS
62 CE: New transition B. Steffen Summer School CPS
63 CE: New transition B. Steffen Summer School CPS
64 Experimental Evaluation B. Steffen Summer School CPS
65 Modeling Output explicitly: RMMs RA RMM is in language Example: Stack of capacity 3 RA: output encoded as guarded transition RMM: output with data for transitions leads to output B. Steffen Summer School CPS
66 RMM: Explicit Output B. Steffen Summer School CPS
67 RMM: Explicit Output Query: push(p 1 )push(p 2 )pop() / p 2 push(p), pop() OK, NOK, null, p stack.push(51) stack.push(2012) stack.pop() true, false, null, 51, 2012 B. Steffen Summer School CPS
68 Inferring RMMs Example: Nested stack of capacity 16 RMM: 781 locations, 45k MQ, 9 EQ, 20 sec. Mealy, D =4: > 10 9 states B. Steffen Summer School CPS
69 Outline Background Manual Treatment of Data Automated Alphabet Abstraction Refinement Modelling Data Explicitly Conclusions B. Steffen Summer School CPS
70 Conclusions and Perspectives Main Practical Challenges are Search for Counterexamples Counterexample Analysis Question: How much can counter examples tell about a system? We have seen scenarios for (beside the classical locations), Optimal Alphabet Abstraction Optimal Register Allocation Optimal Transition Functions We have seen how to get From DFA to Interface Programs or From Languages to Program Executions B. Steffen Summer School CPS
71 Conclusions and Perspectives Beyond: Investigation of language extensions Extended Guards Actions with Effect Procedural Structure? Hybrid Approaches and Case Studies Experimental Evaluation and Performance Analysis The RERS Greybox Challenge 2014 B. Steffen Summer School CPS
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