Related papers: Applications of the Gauss-Jordan algorithm, done r…
The $\lambda$-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
In mathematics, LaTeX is the de facto standard to prepare documents, e.g., scientific publications. While some formulae are still developed using pen and paper, more complicated mathematical expressions used more and more often with…
So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming,…
Abstract interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we…
Geometric algebra (GA) is a mathematical tool for geometric computing, providing a framework that allows a unified and compact approach to geometric relations which in other mathematical systems are typically described using different more…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…
This paper summarises the results obtained by the author and his collaborators in a program logic approach to the verification of quantum programs, including quantum Hoare logic, invariant generation and termination analysis for quantum…
We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra 1(2), 1973, pp. 163-171]. Our algorithms are based on…
In this note, we extend modular techniques for computing Gr\"obner bases from the commutative setting to the vast class of noncommutative $G$-algebras. As in the commutative case, an effective verification test is only known to us in the…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Students of our department solve algebraic exercises in mathematical logic in a computerized environment. They construct transformations step by step and the program checks the syntax, equivalence of expressions and completion of the task.…
In this paper, we propose an algebraic formalization of the two important classes of dynamic programming algorithms called forward and forward-backward algorithms. They are generalized extensively in this study so that a wide range of other…
Modular algorithm are widely used in computer algebra systems (CAS), for example to compute efficiently the gcd of multivariate polynomials. It is known to work to compute Groebner basis over $\Q$, but it does not seem to be popular among…
To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number of simple stereotyped operations, which are adequately…