CalCS: SMT solving for non-linear convex constraints
Pierluigi Nuzzo,Alberto Puggelli,Sanjit A. Seshia,Alberto Sangiovanni-Vincentelli +3 more
- pp 71-80
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TLDR
This paper presents a new technique for satisfiability solving of Boolean combinations of non-linear constraints that are convex, and applies fundamental results from the theory of convex programming to realize a satisfiability modulo theory (SMT) solver.Abstract:
Certain formal verification tasks require reasoning about Boolean combinations of non-linear arithmetic constraints over the real numbers. In this paper, we present a new technique for satisfiability solving of Boolean combinations of non-linear constraints that are convex. Our approach applies fundamental results from the theory of convex programming to realize a satisfiability modulo theory (SMT) solver. Our solver, CalCS, uses a lazy combination of SAT and a theory solver. A key step in our algorithm is the use of complementary slackness and duality theory to generate succinct infeasibility proofs that support conflict-driven learning. Moreover, whenever non-convex constraints are produced from Boolean reasoning, we provide a procedure that generates conservative approximations of the original set of constraints by using geometric properties of convex sets and supporting hyperplanes. We validate CalCS on several benchmarks including formulas generated from bounded model checking of hybrid automata and static analysis of floating-point software.read more
Citations
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Book ChapterDOI
dReal: an SMT solver for nonlinear theories over the reals
TL;DR: The open-source tool dReal is described, an SMT solver for nonlinear formulas over the reals, which can handle various nonlinear real functions such as polynomials, trigonometric functions, exponential functions, etc.
Journal ArticleDOI
Secure State Estimation for Cyber-Physical Systems Under Sensor Attacks: A Satisfiability Modulo Theory Approach
Yasser Shoukry,Pierluigi Nuzzo,Alberto Puggelli,Alberto Sangiovanni-Vincentelli,Sanjit A. Seshia,Paulo Tabuada +5 more
TL;DR: In this article, the authors present a secure state estimation algorithm that uses a satisfiability modulo theory approach to harness the complexity of the secure state estimator and provide guarantees on the soundness and completeness of the algorithm.
Proceedings ArticleDOI
Taylor Model Flowpipe Construction for Non-linear Hybrid Systems
TL;DR: This paper provides techniques for handling the effect of discrete transitions on Taylor model flow pipe construction and explores various solutions based on two ideas: domain contraction and range over-approximation.
Book ChapterDOI
δ-complete decision procedures for satisfiability over the reals
TL;DR: The notion of δ-complete decision procedures for solving SMT problems over real numbers was introduced in this article, with the aim of handling a wide range of nonlinear functions including transcendental functions and solutions of Lipschitzcontinuous ODEs.
Posted Content
Secure State Estimation For Cyber Physical Systems Under Sensor Attacks: A Satisfiability Modulo Theory Approach
Yasser Shoukry,Pierluigi Nuzzo,Alberto Puggelli,Alberto Sangiovanni-Vincentelli,Sanjit A. Seshia,Paulo Tabuada +5 more
TL;DR: A novel algorithm is presented that uses a satisfiability modulo theory approach to harness the complexity of secure state estimation and leverages results from formal methods over real numbers to provide guarantees on the soundness and completeness of the algorithm.
References
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