Optimization of Lyapunov Invariants in Verification of Software Systems
Author(s)Roozbehani, Mardavij; Megretski, Alexandre; Feron, Eric
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The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions and the associated computational techniques from control systems analysis and convex optimization to verification of various software safety and performance specifications. These include but are not limited to absence of overflow, absence of division-by-zero, termination in finite time, absence of dead-code, and certain user-specified assertions. Central to this framework are Lyapunov invariants. These are properly constructed functions of the program variables, and satisfy certain properties-analogous to those of Lyapunov functions-along the execution trace. The search for the invariants can be formulated as a convex optimization problem. If the associated optimization problem is feasible, the result is a certificate for the specification.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
IEEE Transactions on Automatic Control
Institute of Electrical and Electronics Engineers (IEEE)
Roozbehani, M., A. Megretski, and E. Feron. “Optimization of Lyapunov Invariants in Verification of Software Systems.” IEEE Trans. Automat. Contr. 58, no. 3 (March 2013): 696–711.