Almost EventRate Independent Monitoring of Metric Temporal Logic

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Almost Event-Rate Independent Monitoring of Metric Temporal Logic David Basin, Bhargav Bhatt, and Dmitriy

Almost Event-Rate Independent Monitoring of Metric Temporal Logic David Basin, Bhargav Bhatt, and Dmitriy Traytel ETH Zurich Bhargav Bhatt | 27. 04. 2017 | 1

Online Monitoring Problem Property: check if CHF/EUR has been increasing since the fall of

Online Monitoring Problem Property: check if CHF/EUR has been increasing since the fall of SEK/EUR within the previous 3 hours. EVENTS Timepoints: 1 09: 0 Timestamps: 0 ↑CHF Propositions: ↓SEK 2 10: 0 0 ↑CHF ↑SEK 3 12: 0 0 ↓CHF ↑SEK 18: 0 0 ↓CHF ↓SEK MONITOR: VERDICTS: Or Bhargav Bhatt | 27. 04. 2017 | 2

Properties That Talk About The Future Traditional Monitor t 0 t 1 t 5

Properties That Talk About The Future Traditional Monitor t 0 t 1 t 5 t 2 t 3 t 4 Out of Memory Output @t 0: @t 1: @t 2: @t 3: Bhargav Bhatt | 27. 04. 2017 | 3

Our Contribution A New Monitor t 0 t 1 t 2 Output @t 1=

Our Contribution A New Monitor t 0 t 1 t 2 Output @t 1= @t 2 @t 0: @t 3: @t 1: @t 4= @t 5 t 3 t 4 t 5 . . . Number of events in monitor’s buffer dependent only on property, not on trace . . . Bhargav Bhatt | 27. 04. 2017 | 4

MTL : Syntax and Semantics Atomic Propositions (Events) Boolean operators Semantics of Since Property:

MTL : Syntax and Semantics Atomic Propositions (Events) Boolean operators Semantics of Since Property: check if CHF/USD has been increasing since the fall SEK/USD within the previous 3 hours. Temporal operators : Since, Until Intervals over integers, e. g. [2, 7] , [3, ∞) Semantics of Until ↑CHF ↓SEK Bhargav Bhatt | 27. 04. 2017 | 5

Overview Past-MTL Trace-Length Independence Event-Rate Independence State of the art monitoring algorithms MTL (Past

Overview Past-MTL Trace-Length Independence Event-Rate Independence State of the art monitoring algorithms MTL (Past and Future) Trace-Length Independence State of the art monitoring algorithms Almost* Event-Rate Independence ? ? AERIAL Bhargav Bhatt | 27. 04. 2017 | 6

Trace-length Independence (TLI) Space complexity Formula-size Time complexity Trace-length Bhargav Bhatt | 27. 04.

Trace-length Independence (TLI) Space complexity Formula-size Time complexity Trace-length Bhargav Bhatt | 27. 04. 2017 | 7

Trace-length Independence (TLI) independent of timepoint Timepoints: 1 2 i 3 i+1 Verdicts: Event-rate

Trace-length Independence (TLI) independent of timepoint Timepoints: 1 2 i 3 i+1 Verdicts: Event-rate Independence (ERI) 07: 0 0 1 M events 08: 0 0 09: 0 0 10: 00 5 M events 10 M events 4 M events Bhargav Bhatt | 27. 04. 2017 | 8

Overview ? ? Past Future Bhargav Bhatt | 27. 04. 2017 | 9

Overview ? ? Past Future Bhargav Bhatt | 27. 04. 2017 | 9

Our Approach Previous Approaches Why are Future operators difficult? Depends on event-rate. or i

Our Approach Previous Approaches Why are Future operators difficult? Depends on event-rate. or i Verdict: Monitors that output verdicts in order are not ERI. eg. : Monpoly j or or = @i = @j ‘Equivalence’ verdicts * Logarithmic space in event-rate needed to store j as a number Bhargav Bhatt | 27. 04. 2017 | 10

AERIAL (Almost Event Rate Independent MTL monitoring) Dynamic Programming Based Technique using the recursive

AERIAL (Almost Event Rate Independent MTL monitoring) Dynamic Programming Based Technique using the recursive equations characterizing Since and Until : Past: Previous Timepoint Future: Next Timepoint Bhargav Bhatt | 27. 04. 2017 | 11

AERIAL (Almost Event Rate Independent MTL monitoring) • Algorithm can be seen as a

AERIAL (Almost Event Rate Independent MTL monitoring) • Algorithm can be seen as a series of refinements Step 2 : MTL (Past and Future) Step 1 : Past-MTL Step 0 : Past-LTL Bhargav Bhatt | 27. 04. 2017 | 12

Step 2 0 : Add Past support LTL (Havelund and Rosu, 2002) 1 for

Step 2 0 : Add Past support LTL (Havelund and Rosu, 2002) 1 for Future Past-MTL 1 2 3 4 5 T T F F T T F bexp T bexp Boolean Expressions with variables pointing to next column x 1 ⋀ x 2 ⋀ x 1 Verdict: = @i Bhargav Bhatt | 27. 04. 2017 | 13

Experimental Evaluation Bhargav Bhatt | 27. 04. 2017 | 14

Experimental Evaluation Bhargav Bhatt | 27. 04. 2017 | 14

Conclusion • theoretically interesting and New Notion: Event-Rate Independence practically relevant for monitoring in

Conclusion • theoretically interesting and New Notion: Event-Rate Independence practically relevant for monitoring in Big Data domains • New Algorithm: AERIAL, a monitor for MTL New Idea: Out of order • In-order output • Boolean or Equivalence verdicts • Space consumption linear in event-rate logarithmic • Future Work: Extend technique to more expressive logics (for timed properties) Bhargav Bhatt | 27. 04. 2017 | 15

Thank You Almost Event-Rate Independent Monitoring of of Metric Temporal Logic David Basin, Bhargav

Thank You Almost Event-Rate Independent Monitoring of of Metric Temporal Logic David Basin, Bhargav Bhatt, and Dmitriy Traytel ETH Zurich Bhargav Bhatt | 27. 04. 2017 | 16

Conclusion Bhargav Bhatt | 27. 04. 2017 | 17

Conclusion Bhargav Bhatt | 27. 04. 2017 | 17

Unbounded Event-Rate Timepoints: 1 2 3 4 5 6 7 8 9 . .

Unbounded Event-Rate Timepoints: 1 2 3 4 5 6 7 8 9 . . . 10 11 (Event, Timestamp): (e 1, 1) (e 2, 1) (e 3, 2) (e 4, 2) (e 5, 2) (e 6, 2) (e 7, 3) (e 8, 3) (e 9, 3) (e 10, 3)(e 11, 3) (e, t) is repeated 2 t times . . . Event-Rate is roughly half of Trace-Length at any timepoint • On this trace: Event-Rate dependence Trace-Length dependence • TLI and ERI coincide on unbounded event-rate traces • None of the existing monitors are TLI on unbounded Event-Rate traces. Bhargav Bhatt | 27. 04. 2017 | 18