An interval-based SAT modulo ODE solver for model checking nonlinear hybrid systems

• DOI: 10.1007/s10009-011-0193-y
• Publication Date: 2011-03-18T19:16:37Z
• Authors: Daisuke Ishii; Kazunori Ueda; Hiroshi Hosobe
• Keywords: Solver; Satisfiability Modulo Theories; Boolean satisfiability problem; Satisfiability; Reachability problem; Theory of computation; Ode

This paper presents a bounded model checking tool called $${\texttt{Hydlogic}}$$ for hybrid systems. It translates a reachability problem of a nonlinear hybrid system into a predicate logic formula involving arithmetic constraints and checks the satisfiability of the formula based on a satisfiability modulo theories method. We tightly integrate (i) an incremental SAT solver to enumerate the possible sets of constraints and (ii) an interval-based solver for hybrid constraint systems (HCSs) to solve the constraints described in the formulas. The HCS solver verifies the occurrence of a discrete change by using a set of boxes to enclose continuous states that may cause the discrete change. We utilize the existence property of a unique solution in the boxes computed by the HCS solver as (i) a proof of the reachability of a model and (ii) a guide in the over-approximation refinement procedure. Our $${\texttt{Hydlogic}}$$ implementation successfully handled several examples including those with nonlinear constraints.