SReach: Combing SMT-based Model Checking and Statistical Tests* Presented by Qinsi Wang
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1 SReach: Combing SMT-based Model Checking and Statistical Tests* Presented by Qinsi Wang *Qinsi Wang, Paolo Zuliani, Soonho Kong, Sicun Gao, and Edmund Clarke. SReach: Combining Statistical Tests and Bounded Model Checking for Nonlinear Hybrid Systems with Parametric Uncertainty
2 Probabilistic Bounded Reachability Analysis of S tochastic Hybrid Systems
3 Stochastic Hybrid Systems Application: Biology (e.g. the killerred biological model), Cyber-physical systems (e.g. the quadcopter stabilization control system), Financial models (e.g. insurance pricing systems), and so on. Formalism: Probabilistic hybrid automata (PHA), Stochastic hybrid automata (SHA), General Stochastic hybrid systems (GSHS),
4 SReach considers Hybrid automata with parametric uncertainty unknown parameters, individual differences, noisy data, learning errors, Probabilistic hybrid automata transitions with discrete probability distributions transitions with continuous distributions, but discrete choices 4
5 SReach can handle Probabilistic bounded reachability problems One of the elementary questions for the quantitative analysis of stochastic hybrid systems is to compute the probability of reaching a certain set of states. More specifically, model validation, parameter estimation, and sensitivity analysis
6 SReach answers SReach can answer two types of questions: () Does the model satisfy a given reachability property with probability greater than a certain threshold? hypothesis testing (2) What is the probability that the model satisfies a given reachability property? statistical estimation
7 SReach s algorithm
8 SReach uses The following statistical tests: Hypothesis testing methods: Lai s test, Bayes factor test, Bayes factor test with indifference region, and Sequential probability ratio test. Statistical estimation methods: Chernoff- Hoeffding bound, Bayesian interval estimation with beta prior, and Direct sampling.
9 Hybrid automaton with parametric uncertainty
10 Probabilistic Hybrid Automaton DNA= DNAƛ=0 mrna=0 KRim=0 KRm=0 KRmdS=0 KRmdS*=0 KRmdT*=0 SOX=0 SOXsod=0 SOD=SODinit mode_t >= t_genk Genome injected, k ƛgenome= DNA= DNAƛ=0 mrna=0 KRim=0 KRm=0 KRmdS=0 KRmdS*=0 KRmdT*=0 SOX=0 SOXsod=0 SOD=SODinit mode_t >= t_genk2 Genome inserted, k2 mrna=0 KRim=0 KRm=0 KRmdS=0 KRmdS*=0 KRmdT*=0 SOX=0 SOXsod=0 SOD=SODinit mode_t >= t_addiptg Add IPTG IPTG= mrna=? KRim=? KRm=? KRmdS=? KRmdS*=0 KRmdT*=0 SOX=0 SOXsod=0 SOD=SODinit mode_t >= t_rmiptg (and (mrna = 0) (KRim = 0) (KRmdS = 0)) reset mode_t *Natasa Miskov-Zivanov, Qinsi Wang, Cheryl Telmer, Edmund M. Clarke, et al. Formal analysis estimates parameters for guiding hyperoxidation in bacteria with KillerRed protein. 0. Remove IPTG mrna=a KRim=b KRm=c KRmdS=d KRmdS*=0 KRmdT*=0 SOX=0 SOXsod=0 SOD=SODinit mode_t >= t_lighton 0.9 Add light IPTG= light=l mrna=? KRim=? KRm=? KRmdS=? KRmdS*=? KRmdT*=? SOX=? SOXsod=? SOD=? SOX>threshold & tot_t <= timebound 0.4 mode_t >= t_rmiptg2 -p Remove IPTG & reset mode_t mode_t >= t_lightoff 0.3 mode_t >= t_rmiptg2 0.3 Remove IPTG Remove light SOX>threshold & tot_t <= timebound p2~ B(0.9) cell death IPTG= mrna=? KRim=? KRm=? KRmdS=? KRmdS*=? KRmdT*=? SOX=g SOXsod=h SOD=i light=l mrna=a KRim=b KRm=c KRmdS=d KRmdS*=e KRmdT*=f SOX=g SOXsod=h SOD=i mode_t >= t_rmiptg3 mode_t >= t_lightoff2 p ~ U(0, ) -p2 Remove IPTG Remove light mrna=a KRim=b KRm=c KRmdS=d KRmdS*=e KRmdT*=f SOX=g SOXsod=h SOD=i mrna=a KRim=b KRm=c KRmdS=d KRmdS*=e KRmdT*=f SOX=g SOXsod=h SOD=i SOX>threshold & tot_t <= timebound SOX>threshold & tot_t <= timebound. Will the killerred kill bacteria cells within a certain time with probability no less then 0.95? 2. Will the time duration that keeps the light on impact the whole process significantly? What will be relation between the time to turn on the light and the time needed to kill bacteria cells?
11 Experimental results
12 Future work General Stochastic Hybrid Systems probabilistic jumps with continuous distributions stochastic flows: stochastic differential equations Propose and implement a new theory solver for a subset of probability theory
13 Thanks, Ed! paralleled version will be released soon!
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