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Many types of formal verification establish properties about abstract high-level program representations, leaving a large gap to programs at runtime. Although gaps can sometimes be narrowed by techniques such as refinement, a verified…
We present a new software tool for teaching logic based on natural deduction. Its proof system is formalized in the proof assistant Isabelle such that its definition is very precise. Soundness of the formalization has been proved in…
Word-level verification of arithmetic circuits with large operands typically relies on arbitrary-precision arithmetic, which can lead to significant computational overhead as word sizes grow. In this paper, we present a hybrid algebraic…
Proof assistants are computer softwares that allow us to write mathematical proofs so as to assess their correctness. In November 2021, I started the project of checking the simplicity of the alternating groups within the Lean theorem…
We formalize the univariate fragment of Ben-Or, Kozen, and Reif's (BKR) decision procedure for first-order real arithmetic in Isabelle/HOL. BKR's algorithm has good potential for parallelism and was designed to be used in practice. Its key…
Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
In this paper, we describe general characteristics of the MathPartner computer algebra system (CAS) and Mathpar programming language thereof. MathPartner can be used for scientific and engineering calculations, as well as in high schools…
Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…
Isabelle2Cpp is a code generation framework that supports automatic generation of C++ code from Isabelle/HOL specifications. However, if some type information of Isabelle/HOL specification is missing, Isabelle2Cpp may not complete the code…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
This is an overview of the Paral-ITP project, which intents to make the proof assistants Isabelle and Coq fit for the multicore era.
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
Hopf algebraic structures will replace groups and group representations as the leading paradigm in forthcoming times. K-theory, co-homology, entanglement, statistics, representation categories, quantized or twisted structures as well as…
Diagnosability is a system theoretical property characterizing whether fault occurrences in a system can always be detected within a finite time. In this paper, we investigate the verification of diagnosability for cyber-physical systems…
Performant numerical solving of differential equations is required for large-scale scientific modeling. In this manuscript we focus on two questions: (1) how can researchers empirically verify theoretical advances and consistently compare…
This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…
Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…