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Efficient Decentralized Monitoring of Safety in Distributed Systems

This paper discusses an efficient decentralized monitoring approach for ensuring safety in distributed systems. It explores the use of formal methods, such as model checking and theorem proving, to synthesize lightweight monitors from specifications. The monitoring algorithm utilizes Knowledge Vectors attached to outgoing messages and updates Knowledge Vectors with incoming messages, ensuring minimal memory overhead and additional message sends.

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Efficient Decentralized Monitoring of Safety in Distributed Systems

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  1. Efficient Decentralized Monitoring of Safety in Distributed Systems Koushik Sen Abhay Vardhan Gul Agha Grigore Rosu University of Illinois at Urbana-Champaign, USA

  2. Software Reliability • Software Validation • Rigorous and Complete Methods • Model Checking • Theorem Proving • Infeasible for large-scale open distributed systems • Non-determinism and Asynchrony • Testing • Widely used • Ad-Hoc • Good Test Coverage Required • Runtime Monitoring • Adds rigor to Testing

  3. Centralized Monitoring Approach • Monitoring – Use Formal Methods in Testing • Synthesize light-weight Monitors from Specification • Automata, Rewriting-based Monitors, State machines • Instrument code to insert monitors • Execute instrumented code • Distributed System Monitoring • Global state is distributed • For every state update send state to a central monitor • Central monitor assembles them to form consistent execution traces (Vector Clocks) • Sequence of global states • Monitor execution traces

  4. An Example • Mobile node a requests certain value from node b • b computes the value and sends it to a • Property: no node receives a value from another node to which it had not sent a request

  5. Centralized Monitoring Example “If a receives a value from b then b calculated the value after receiving request from a” valRcv → (valComputed  valReq) valReq valReq valComputed  valReq valRcv → (valComputed  valReq) (valComputed  valReq) Monitor b valComputed a valReq valRcv

  6. Decentralized Monitoring Approach “If a receives a value from b then b calculated the value after receiving request from a” valRcv → @b((valComputed  @a(valReq))) valComputed  @a(valReq) @a(valReq) (valComputed  @a(valReq)) b valComputed a valReq valRcv valReq valRcv → @b((valComputed  @a(valReq)))

  7. Past time Distributed Temporal Logic (pt-DTL) • Past Time Linear Temporal Logic [Pnueli] • Extended with a Operator from epistemic logic (@) • [Aumann76][Meenakshi et al. 00] • Properties with respect to a process, say p • Interpreted over sequence of knowledge that p has about global state

  8. Remote Formulas in pt-DTL • @a F at process b • @ makes remote formula F at process a local to process b “Alarm at process b implies that there was a fire at a” alarm → @afire a formula with respect to process b

  9. Remote Expressions in pt-DTL • Remote expressions – arbitrary expressions related to the state of a remote process • Propositions constructed from remote and local expressions “If my alarm is set then eventually in past difference between my temperature and temperature at process b exceeded the allowed value” alarm → ((myTemp - @btemp) > allowed)

  10. Safety in Airplane Landing “ If my airplane is landing then the runway that the airport has allocated matches the one that I am planning to use” landing → (runway = @airportallocRunway)

  11. Leader Election Example “If a leader is elected then if the current process is a leader then, at its knowledge, none of the other processes is a leader” elected → (state=leader → /\i≠j(@j(state ≠ leader)))

  12. pt-DTL syntax • Fi ::= true | false | P(Ei) | : Fi | FiÆ Fi propositional | ¯ Fi | ¡ Fi | Fi | Fi S Fi temporal | @jFj epistemic • Ei ::= c | vi2 Vi | f(Ei) functional | @jEj epistemic

  13. Interpretation of @jEj at process i p3 m4 m1 m2 p2 @ 1(x=9) m3 p1 x=7 x=9

  14. Monitoring Algorithm • Requirements • Should be fast so that online monitoring is possible • Little memory overhead • Additional messages sent should be minimal; ideally zero

  15. KnowledgeVector Let KV be a vector • one entry for each process appearing in formula • KV[j] denotes entry for process j • KV[j].seq is the sequence number of last event seen at process j • KV[j].values stores values of j-expressions and j-formulae

  16. Monitoring using KnowledgeVector • Maintain KnowledgeVector about global state at each process • Attach KnowledgeVector with outgoing messages • Update KnowledgeVector with incoming messages • At each process monitor local KnowledgeVector

  17. KnowledgeVector Algorithm • [internal event]: (at process i) store eval(Ei,si) and eval(Fi,si) for each @iEi and @iFi in KVi[i].values • [send m]: KVi[i].seq à KVi[i].seq + 1. Send KVi with m as KVm • [receive m]: for all j, if KVm[j].seq > KVi[j].seq then • KVi[j].seq à KVm[j].seq • KVi[j].values à KVm[j].value • store eval(Ei,si) and eval(Fi,si) for each @iEi and @iFi in KVi[i].values

  18. 0 2 2 2 2 0 2 0 1 1 2 0 6 9 6 6 6 6 5 6 5 6 5 9 Example p3 p2 Y=7 Y=3 violation p1 X=5 X=9 X=6 KV[1].seq ¡(Y¸ @1X) at p2 KV[1].values

  19. DIANA Architecture pt-DTL Monitor

  20. Conclusion • pt-DTL can express interesting and useful safety properties of distributed systems • Decentralized Technique to effectively verify Distributed Systems at runtime • No extra message over-head for monitoring • KnowledgeVector as monitors

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