Related papers: Towards the Certification of Complexity Proofs
In this Masters thesis we present an implementation of a fragment of "book HoTT" as an object logic for the interactive proof assistant Isabelle. We also give a mathematical description of the underlying theory of the Isabelle/Pure logical…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
This paper describes a formal theory of smooth vector fields, Lie groups and the Lie algebra of a Lie group in the theorem prover Isabelle. Lie groups are abstract structures that are composable, invertible and differentiable. They are…
The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three…
This is the second installment of an exposition of an ACL2 formalization of elementary linear algebra. It extends the results of Part I, which covers the algebra of matrices over a commutative ring, but focuses on aspects of the theory that…
When we want to answer/certify whether a given equation is entailed by an equational system we face the following problems: (1) It is hard to find a conversion (but easy to certify a given one). (2) Under the assumption that Knuth-Bendix…
Complex systems typically have many different parts and facets, with different characteristics. In a multi-paradigm approach to modeling, formalisms with different natures are used in combination to describe complementary parts and aspects…
Mission-time Linear Temporal Logic (MLTL), a widely used subset of popular specification logics like STL and MTL, is often used to model and verify real world systems in safety-critical contexts. As the results of formal verification are…
A method is provided for computing an upper bound of the complexity of a module over a local ring, in terms of vanishing of certain cohomology modules. We then specialize to complete intersections, which are precisely the rings over which…
This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.
This set of theories presents an Isabelle/HOL+Isar formalisation of stream processing components introduces in Focus, a framework for formal specification and development of interactive systems. This is an extended and updated version of…
We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification…
We have formalised Szemer\'edi's Regularity Lemma and Roth's Theorem on Arithmetic Progressions, two major results in extremal graph theory and additive combinatorics, using the proof assistant Isabelle/HOL. For the latter formalisation, we…
Simulation and formal verification are important complementary techniques necessary in high assurance model-based systems development. In order to support coherent results, it is necessary to provide unifying semantics and automation for…
Matrix interpretations generalize linear polynomial interpretations and have been proved useful in the implementation of tools for automatically proving termination of Term Rewriting Systems. In view of the successful use of rational…
The q-generalizations of the two fundamental statements of matrix algebra -- the Cayley-Hamilton theorem and the Newton relations -- to the cases of quantum matrix algebras of an "RTT-" and of a "Reflection equation" types have been…
This paper explores verification of constituent systems within the context of the Symphony tool platform for Systems of Systems (SoS). Our SoS modelling language, CML, supports various contractual specification elements, such as state…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…