Synthesizing More Expressive Invariants by Semidefinite Programming.

Invariant generation plays a central role in the verification of programs and hybrid systems. In this paper, we propose an approach to synthesize invariants using semidefinite programming (SDP) that combine advantages of both symbolic constraint solving and numeric constraint solving. The advantages of our approach is threefold: first, it is powerful enough that can be applied to arbitrary predefined templates as symbolic computation based techniques do; second, it uses semidefinite programming instead of time-consuming symbolic subroutines and is therefore efficient enough as other numeric computation based techniques are; lastly, it can also have some (although weaker) theoretical guarantees of completeness as those symbolic computation based techniques have. In addition, we discuss how to generalize our approach to the case when templates are semialgebraic instead of polynomial and the case when non-polynomial functions such as trigonometric functions, logarithmic functions, exponential functions, rational functions are present in programs.