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

Abstract

Abstract. This paper presents a bounded model checking (BMC) tool called 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 (SMT) 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 enclosing continuous states that may cause the discrete change by a set of boxes. We adopt 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 hydlogic implementation successfully handled several examples including those with nonlinear constraints.

Deductive software verification

“…There are so many techniques and tools related to formal methods that one can quickly get lost. In the five papers of this special issue [15,16,26,30,53], I could enumerate not less than 65 different tools and languages being cited. At least, half of them were indeed used by the authors, not mentioning the design and implementation of new tools [16,30] or languages [53].…”

“…An Interval-based SAT Modulo ODE Solver for Model Checking Nonlinear Hybrid Systems [30] is introducing hydlogic, a new bounded model checker for hybrid systems. Such systems combine discrete and continuous models, to describe programs which interact with physical environments.…”

A verified method for solving piecewise smooth initial value problems

“…Further interesting references are the works of Goldsztejn et al (2010), Ramdani and Nedialkov (2011), Ishii et al (2011), Zgliczynski and Kapela (2009), or Galias (2012.…”

Improving SAT Modulo ODE for Hybrid Systems Analysis by Combining Different Enclosure Methods

“…As the reported candidate solution boxes are very small, interval Newton methods may be able to verify that they contain an actual solution. While our algorithm currently does not contain such a check, Ishii et al [8] have implemented it.…”

“…al. [8] in a traditional Satisfiability Modulo Theories (SMT) scheme. In contrast to such an integration (i.e., a SAT solver selecting which theory atoms shall be satisfied, interleaved with theory solvers evaluating this conjunction of atoms), the iSAT [5] algorithm performs a search by splitting intervals and hence indirectly ruling out those atoms that become inconsistent under this valuation, and thus deducing that other arithmetic constraints must be satisfied for satisfaction of the entire formula.…”