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Invariant synthesis plays a central role in the verification of programs. In this paper, we propose a novel approach to synthesize basic semialgebraic invariants using semidefinite programming (SDP) that combines advantages of both symbolic constraint solving methods and numeric constraint solving methods. The advantages of our approach are threefold: first, it can deal with arbitrary templates as symbolic computation based techniques; second, it uses SDP instead of computationally intensive symbolic subroutines and is therefore efficient enough as other numeric computation based techniques; lastly, there are some (although weaker) theoretical guarantees on its completeness, which previously can only be provided by symbolic computation based techniques.
Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discove
The tendency of semidefinite programs to compose perfectly under product has been exploited many times in complexity theory: for example, by Lovasz to determine the Shannon capacity of the pentagon; to show a direct sum theorem for non-deterministic
Finding exact Ramsey numbers is a problem typically restricted to relatively small graphs. The flag algebra method was developed to find asymptotic results for very large graphs, so it seems that the method is not suitable for finding small Ramsey nu
Semidefinite Programming (SDP) is a class of convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization and operational research. Noisy intermediate-scale quantum (NISQ) algorithms aim to ma
Block-based visual programming environments play a critical role in introducing computing concepts to K-12 students. One of the key pedagogical challenges in these environments is in designing new practice tasks for a student that match a desired lev