Related papers: Multi-Sequential Word Relations
It is shown that the DFT exchange and correlation functionals satisfy an expression that couples exchange and correlation functionals and functional derivatives evaluated at three different densities and for two particle numbers. This…
Let $B$ be a fixed rational function of one complex variable of degree at least two. In this paper, we study solutions of the functional equation $A\circ X=X\circ B$ in rational functions $A$ and $X$. Our main result states that, unless $B$…
Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of…
Automata-logic connections are pillars of the theory of regular languages. Such connections are harder to obtain for transducers, but important results have been obtained recently for word-to-word transformations, showing that the three…
In quantum logic there is well-known arbitrariness in choosing a binary operation for conditional. Currently, we have at least three candidates, called the Sasaki conditional, the contrapositive Sasaki conditional, and the relevance…
Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models…
Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
Well-known principles of induction include monotone induction and different sorts of non-monotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
We study the separability problem for automatic relations (i.e., relations on finite words definable by synchronous automata) in terms of recognizable relations (i.e., finite unions of products of regular languages). This problem takes as…
Relational thinking refers to the inherent ability of humans to form mental impressions about relations between sensory signals and prior knowledge, and subsequently incorporate them into their model of their world. Despite the crucial role…
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
Vision foundation models (FMs) have become the predominant architecture in computer vision, providing highly transferable representations learned from large-scale, multimodal corpora. Nonetheless, they exhibit persistent limitations on…
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the…
This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as…
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as…
Recently, Gavazzo has developed a relational theory of symbolic manipulation, that allows to study syntax-based rewriting systems without relying on specific notions of syntax. This theory was obtained by extending the algebra of relations…
Taking an interaction network oriented perspective in informatics raises the challenge to describe deterministic finite systems which take part in networks of nondeterministic interactions. The traditional approach to describe processes as…