A Non-linear Arithmetic Procedure for Control-Command Software Verification

“…Thus, the software verification in our case focuses on translating the guarantees obtained at the algorithmic level, using the analysis results from [17], and expressing them at the code level. Then, we revalidate the invariant properties at the code level using Alt-Ergo-Poly [28], an extension of the SMT solver Alt-Ergo [8] with a sound Sum-of-Squares solver [27,22], to discharge positive polynomial constraints. Last, we instrument the contract to account for floating-point errors in the code, ensuring the validity of our contracts despite the noise caused by floating-point inaccuracy.…”

Section: Introductionmentioning

confidence: 99%

Code-Level Formal Verification of Ellipsoidal Invariant Sets for Linear Parameter-Varying Systems

Khalife

Garoche

Farhood

2023

Lecture Notes in Computer Science

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This paper focuses on the formal verification of invariant properties of a C code that describes the dynamics of a discrete-time linear parameter-varying system with affine parameter dependence. The C code is annotated using ACSL, and the Frama-C's WP plugin is used to transform the annotations and code into proof objectives. The invariant properties are then formally verified in both the real and float models using the polynomial inequalities plugin of the theorem prover Alt-Ergo. The challenges of verifying the invariant properties in the float model are addressed by utilizing bounds on numerical errors and incorporating them into the real model.

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“…This approach introduces a clear advantage over SMT solvers by including support for the decidable theory of the real closed fields. Other efforts for efficient reasoning about polynomials can be found in Yices 2 [12] and Alt-Ergo [30]. From the computer algebra standpoint, Mathematica and Maple have been the tools of choice for symbolic reasoning in nonlinear arithmetic.…”

Section: Introductionmentioning

confidence: 99%

Real-time MTL with durations as SMT with applications to schedulability analysis

Matos

Leucker

Pereira

et al. 2020

2020 International Symposium on Theoretical Aspects of Software Engineering (TASE)

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This paper introduces a synthesis procedure for the satisfiability problem of RMTL-formulas as SAT solving modulo theories. RMTL-is a real-time version of metric temporal logic (MTL) extended by a duration quantifier allowing to measure time durations. For any given formula, a SAT instance modulo the theory of arrays, uninterpreted functions with equality and non-linear real-arithmetic is synthesized and may then be further investigated using appropriate SMT solvers. We show the benefits of using RMTL-with the given SMT encoding on a diversified set of examples that include in particular its application in the area of schedulability analysis. Therefore, we introduce a simple language for formalizing schedulability problems and show how to formulate timing constraints as RMTLformulas. Our practical evaluation based on our synthesis and Z3 as back-end SMT solver also shows the feasibility of the overall approach.

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A Non-linear Arithmetic Procedure for Control-Command Software Verification

Cited by 6 publications

References 38 publications

Preserving Functional Correctness of Cyber-Physical System Controllers: From Model to Code

Preserving Functional Correctness of Cyber-Physical System Controllers: From Model to Code

Code-Level Formal Verification of Ellipsoidal Invariant Sets for Linear Parameter-Varying Systems

Real-time MTL with durations as SMT with applications to schedulability analysis

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