Related papers: Formalization of Complex Vectors in Higher-Order L…

A thorough discussion and development of the calculus of real-valued functions of complex-valued vectors is given using the framework of the Wirtinger Calculus. The presented material is suitable for exposition in an introductory Electrical…

A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…

Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure.…

An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…

Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…

Synthetic Biology is an interdisciplinary field that utilizes well-established engineering principles, ranging from electrical, control and computer systems, for analyzing the biological systems, such as biological circuits, enzymes,…

For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…

Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…

Chemical theory can be made more rigorous using the Lean theorem prover, an interactive theorem prover for complex mathematics. We formalize the Langmuir and BET theories of adsorption, making each scientific premise clear and every step of…

Modeling and analysis of soft errors in electronic circuits has traditionally been done using computer simulations. Computer simulations cannot guarantee correctness of analysis because they utilize approximate real number representations…

Simulink is a graphical environment that is widely adapted for the modeling and the Laplace transform based analysis of linear analog circuits used in signal processing architectures. However, due to the involvement of the numerical…

Vector representations have become a central element in semantic language modelling, leading to mathematical overlaps with many fields including quantum theory. Compositionality is a core goal for such representations: given representations…

Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…

Many security- and performance-critical domains, such as cryptography, rely on low-level verification to minimize the trusted computing surface and allow code to be written directly in assembly. However, verifying assembly code against a…

We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…

Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…

We present a mathematical framework for mapping second-order logic relations onto a simple state vector algebra. Using this algebra, basic theorems of set theory can be proven in an algorithmic way, hence by an expert system. We illustrate…

We present a formalization of convex polyhedra in the proof assistant Coq. The cornerstone of our work is a complete implementation of the simplex method, together with the proof of its correctness and termination. This allows us to define…

Advances in vectorial polarisation-resolved imaging are bringing new capabilities to applications ranging from fundamental physics through to clinical diagnosis. Imaging polarimetry requires determination of the Mueller matrix (MM) at every…

In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…