Real Algebraic Strategies for MetiTarski Proofs

Passmore, Grant Olney; Paulson, Lawrence C.; Moura, Leonardo de

doi:10.1007/978-3-642-31374-5_24

Cited by 9 publications

(7 citation statements)

References 10 publications

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“…where untrustedAdd is currently backed up by Grant Passmore's code for algebraic operations in MetiTarski [14]. After such linking, alg_add becomes executable:…”

Section: Enable Executability On Algebraic Realsmentioning

confidence: 99%

A modular, efficient formalisation of real algebraic numbers

Paulson

2016

Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs

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This paper presents a construction of the real algebraic numbers with executable arithmetic operations in Isabelle/HOL. Instead of verified resultants, arithmetic operations on real algebraic numbers are based on a decision procedure to decide the sign of a bivariate polynomial (with rational coefficients) at a real algebraic point. The modular design allows the safe use of fast external code. This work can be the basis for decision procedures that rely on real algebraic numbers.

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“…where untrustedAdd is currently backed up by Grant Passmore's code for algebraic operations in MetiTarski [14]. After such linking, alg_add becomes executable:…”

Section: Enable Executability On Algebraic Realsmentioning

confidence: 99%

A modular, efficient formalisation of real algebraic numbers

Paulson

2016

Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs

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“…The toolset applies proof decomposition in-the-large across multiple verification tools, basing on the completeness of differential dynamic logic (dL [58,61]), which is a real-valued first-order dynamic logic for hybrid programs, a program notation for hybrid systems. Sphinx extends our previous work on the deductive verification tool KeYmaera [65] and on the nonlinear real arithmetic verification tools RAHD [55] and MetiTarski [56] with tools for (i) graphical (UML) modeling, model transformation, and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) exchanging knowledge and tasks through a project management backend. Structure of the paper.…”

Section: Introductionmentioning

confidence: 95%

Collaborative Verification-Driven Engineering of Hybrid Systems

Mitsch¹,

Passmore²,

Platzer³

2014

Math.Comput.Sci.

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Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks

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“…Automatically generated problems tend to be regular, and should if possible be tailored to the strengths of the component that will process them, or conversely, that component could itself be modified to perform better on those automatically generated problems. In the case of Z3, we were able to find a number of refinements that greatly improved its performance with MetiTarski [20]. One such refinement is to switch off a processing stage (univariate polynomial factorisation) that we could predict to be unnecessary.…”

Section: Ongoing Researchmentioning

confidence: 99%