Related papers: On some open problems in Algebraic logic
In this paper, we show how solutions to explicit algebraic systems lead to solutions to infinite families of modular differential equations.
The aim of the paper is to discuss the relations between the three kinds of objects named in the title. In a sense, this is a survey of such relations; however, some new directions are also considered. This relates, especially, to sections…
In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…
Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.
We prove that the main examples in the theory of algebraic differential equations possess a remarkable total differential overconvergence property. This allows one to consider solutions to these equations with coordinates in algebraically…
We further develop the algebraic approach to input/output logic initiated in \cite{wollic22}, where subordination algebras and a family of their generalizations were proposed as a semantic environment of various input/output logics. In…
A new generalization of the classical separate algebraicity theorem is suggested and proved.
In this note, we observe a relation between dialgebras (in particular, Leibniz algebras) and conformal algebras. The purpose is to show how the methods of conformal algebras help solving problems on dialgebras, and, conversely, how the…
A logic is said to admit an equational completeness theorem when it can be interpreted into the equational consequence relative to some class of algebras. We characterize logics admitting an equational completeness theorem that are either…
An algebra-logical repair method for FPGA functional logic blocks on the basis of solving the coverage problem is proposed. It is focused on implementation into Infrastructure IP for system-on-a chip and system-in-package. A method is…
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
We provide a mathematical theory and methodology for synthesising equational logics from algebraic metatheories. We illustrate our methodology by means of two applications: a rational reconstruction of Birkhoff's Equational Logic and a new…
This is a structured compilation of some of my favourite open problems.
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
We report on a collection of open problems in commutative algebra and related areas that have been resolved (proved or disproved) using the Rethlas natural-language automated reasoning system. The problems are drawn from several published…
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
We present here algorithms for efficient computation of linear algebra problems over finite fields.