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Test Plan Generation for Concurrent Real-Time Systems based on Zone Coverage Analysis

Test Plan Generation for Concurrent Real-Time Systems based on Zone Coverage Analysis. Farn Wang Dept. of Electrical Eng. National Taiwan University joint work w. G.-D. Huang. Background. Testing is still the main verification technique.

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Test Plan Generation for Concurrent Real-Time Systems based on Zone Coverage Analysis

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  1. Test Plan Generation for Concurrent Real-Time Systems based on Zone Coverage Analysis Farn Wang Dept. of Electrical Eng. National Taiwan University joint work w. G.-D. Huang TESTCOM/FATES 2008

  2. Background • Testing is still the main verification technique. • CRTS (Concurrent Real-Time Systems) imposes challenges to test coverage. • concurrency  event ordering • event time instances • appropriate coverage mertics for CRTS ? states ? regions ? zones ? TESTCOM/FATES 2008

  3. Proposal • CTA (communicating timed automata) for the model of CRTS • AZC (Active Zone Coverage) • Estimate how big a zone is. • Only active variables are used in determining zones • Testplan for efficient AZC gains • Experiments TESTCOM/FATES 2008

  4. Related work (1/2) • Classic: • statement coverage, visited-state, transition coverage • TA (timed automata) reachability • arc coverage, trigger coverage • region coverage, estimation technique of regions in a zone. • UPPAAL • time-optimal testplans • edge coverage, location coverage, dataflow coverage TESTCOM/FATES 2008

  5. Related work (2/2) • event-recording automata  reachability graph of equivalence classes  test plan • arc coverage, location coverage, domain analysis, dataflow coverage • uniformly priced timed automata  test plans with a minimum cost • Test plan based on fault-detection rate for regression testing • Test case with region coverage annotations for timed automata model TESTCOM/FATES 2008

  6. ?cd ?cd idle 14 !end x2==808 wait !end x1==808 wait 15 13 18 2 9 1 8 17 ?cd ?cd !cd !cd !begin x1=0; !begin x2=0; ?begin x3=0; ?end ?cd ?cd 4 11 send x1<=808 send x2<=808 busy 16 collision x<26 retry x<=52 ?cd retry x<=52 ?cd 5 12 ?begin x3<26 x3=0; !begin x1=0; !begin x2=0; 3 10 Sender 2 Sender 1 Bus Sender1,Sender2, and Bus are all PTAs. CTA Communicating Timed Automata TESTCOM/FATES 2008

  7. CTA LGT (legitimate global transitions) • synchronized: for every event e, every !e is received by exactly a ?e. • minimal: it cannot be decomposed to more than one legitimate global transitions TESTCOM/FATES 2008

  8. ?cd ?cd idle 14 !end x2==808 wait !end x1==808 wait 15 13 18 2 9 1 8 17 ?cd ?cd !cd !cd !begin x1=0; !begin x2=0; ?begin x3=0; ?end ?cd ?cd 4 11 send x1<=808 send x2<=808 busy 16 collision x<26 retry x<=52 ?cd retry x<=52 ?cd 5 12 ?begin x3<26 x3=0; !begin x1=0; !begin x2=0; 3 10 Sender 2 Sender 1 Bus CTA LGT (legitimate global transitions) 19 (1,15) is an LGT. (8,15) is an LGT. (4,13,18) is an LGT. (4) is not. not sync’d (1,8,15) is not. not sync’d (4,18) is not. not sync’d (19,8,15) is not. not minimal TESTCOM/FATES 2008

  9. CTAstates and transitions state , a valuation • from propositions to {true, false} • from clocks to non-negative reals • +t, a state identical to except that for all clocks x, (+t)(x) = (x)+t, transitions g’ • satisfies the trigger of g. • ’ is identical to  except that clocks are reset according to g. TESTCOM/FATES 2008

  10. Regions & Zones • Zones: convex space characterizable with constraints of the form x-y<c, x-y≤c • x,y: clocks or zeros, • c: an integer with |c| ≤ the biggest timing constant used in the model and property. • Regions: the smallest non-empty zones • Region-equivalence is fine enough for TCTL model-checking. • Zone-equivalence can also be fine enough and efficient for the same purpose. TESTCOM/FATES 2008

  11. Symbolic postcondition ’ = post(,g): the zone for the timed postcondition ’ of zone  after LGT g. post(,g)={| ’,tR, t≥0, ’+tg} TESTCOM/FATES 2008

  12. Zone Forestconstruct the reachability graph ZoneForest(A, ) { Rewrite the initial condition of A in DN 1 …  n R:={ 1, … ,n }; V:=R; Φ:=R; K:= ; := 1 …  n ; While , { Pick a zone  from ; let  := – {}; For each LGT g { Let ’ := post( , g); If ’ is satisfiable, { :=  ’; := {’}; V:=V{’}; K:=K  {(,g, ’)}. } } } return (V,R,K); } The reachability predicate already-reachables are not explored. TESTCOM/FATES 2008

  13. Active zones (1/2) • A variable x is active in a state iff there is a run from along which x is read before ever written to. (Write(x)Read(x)) U Read(x) • Write(x), the disjunction of triggers of all LGT g which writes to x. • Read(x), • the disjunction of triggers of all LGT g which reads x in either triggers or the RHS of actions • the invariance condiitons • the risk conditions TESTCOM/FATES 2008

  14. Active zones (2/2) Reduce the representation sizes of reachable spaces! ActiveZone () { for every clock x, if (Write(x)Read(x)) U Read(x) is unsatisfiable, := x(); return ; } Improve performance in ZoneForest construction! Gain more regions in coverage! TESTCOM/FATES 2008

  15. Prioritized Test Plan Generation TestPlan(A, ) { Let  be the set of root-to-leaf paths in ZoneForest(A,  ); Let  be an empty sequence; := false. While   { Pick a 1…n  s.t.  ’1…’m  RCM(ActiveZone(1 …  n )) ≥ RCM(ActiveZone(’1 …  ’m )) :=  - {1…n}; :=  testcase(1…n);  := 1 …  n ; } return  } The region coverage estimation technique in FORTE 2003, by Wang, Hwang, Yu. Sequence concatenation. TESTCOM/FATES 2008

  16. Experiments • RED, version 7.0 • model-checker for TCTL and TAs • simulation-checker for TAs • parametric analyzer for LHAs • In sourceforge project REDLIB. • BLUETOOTH, L2CAP • Linux, REDHAT 9, 3.2GHz We did not compare with other tools. • previous state-based coverage for timed systems ? • could have to concoct some SUTs that show our performance. TESTCOM/FATES 2008

  17. AZC estimation for zone forest construction TESTCOM/FATES 2008

  18. AZC gain for prioritized test plan TESTCOM/FATES 2008

  19. Future work • The strength of state-based coverage for timed systems ? • New state-based coverage metrics for timed systems • Cost of testcases ? TESTCOM/FATES 2008

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