This book constitutes the refereed proceedings of the 13th International Conference on Verified Software, VSTTE 2021, and the 14th International Workshop on Numerical Software Verification, NSV 2021, held online, in July/ October 2021.

VSTTE 2021.- Quantitative Monitoring of Software.- Making Proofs of Floating-Point Programs Accessible to Regular Developers.- A Calculus for Multi-language Operational Semantics.- Partial Order Reduction for Timed Actors.- Uncertainty-Aware Signal Temporal Logic Inference.- Designing and Proving Properties of the Abaco Autoscaler Using TLA+.- Case Study: Analysis of Autonomous Center line Tracking Neural Networks.- Abstract Interpretation of LLVM with a Region-Based Memory Model.- NSV 2021.- Formal Verification of Neural Network Controllers for Collision-Free Flight.- An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods.-Modeling Round-off Errors in Hydrodynamic Simulations.

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