BioPSy

SMT Based Tool for Guaranteed Parameter Set Synthesis

Parameter synthesis?

Formally, parameter synthesis is categorised as a reachability problem, where the solution to a set of ODEs is known for a finite number of time points, but some of the parameter values that lead to that solution are missing.

And since simulation sucks and model checking is hard, we use SMT solving, because then the results are...

guaranteed

How does it work?

Magic! Pardon me, SMT!

SMT Solving

SMT problem is a decision problem for logical formulas with respect to combinations of background theories expressed in classical first-order logic with equality

Human readable: Are there some reals/integers/bitvectors/lists/... that satisfy this first-order logic formula?

The Catch

Solution functions of Lipchitz-continuous ODE systems are computable (over vectors of real numbers), because an approximation of the integral can be computed using a finite number of sums up to the specified precision [1]

Where is the formula?

Conclusion: Formula will contain initial conditions, variable/parameter constrains and integral approximation

[1] S. Gao, S. Kong, E. M. Clarke. Satisfiability Modulo ODEs, CoRR, 2013

So how do you actually solve that?

Lots of interval pruning

1. Define ODEs and variable constrains
2. Solve
3. Profit!    Or not?

Undecidability

Case study

(personalised prostate cancer treatment)

Conclusions

We have a nice SMT solver. I wonder what we can use it for...