Related papers: Word equations, constraints, and formal languages
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
We consider word maps and word maps with constants on a simple algebraic group. We present results on the images of such maps, in particular, we prove a theorem on the dominance of general word maps with constants, which can be viewed as an…
When eating spaghetti, one should have the sauce and noodles mixed instead of eating them separately. We argue that also in string solving, word equations and regular constraints are better mixed together than approached separately as in…
The \emph{word problem} of a group $G = \langle \Sigma \rangle$ can be defined as the set of formal words in $\Sigma^*$ that represent the identity in $G$. When viewed as formal languages, this gives a strong connection between classes of…
It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…
The paper aims at emphasizing that, even relaxed, the hypothesis of compositionality has to face many problems when used for interpreting natural language texts. Rather than fixing these problems within the compositional framework, we…
We give a finite axiomatization for the variety generated by relational, integral ordered monoids. As a corollary we get a finite axiomatization for the language interpretation as well.
This paper (cmp-lg/yymmnnn) has been accepted for publication in the student session of EACL-95. It outlines ongoing work using statistical and unsupervised neural network methods for clustering words in untagged corpora. Such approaches…
Enlarging on Parts I and II we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of full dynamic equations, including equations where the medium is moving or otherwise changing…
By calling into question the implicit structural rules that are taken for granted in classical logic, substructural logics have brought to the fore new forms of reasoning with applications in many interdisciplinary areas of interest.…
We describe a solution of the word problem in free fields (coming from non-commutative polynomials over a commutative field) using elementary linear algebra, provided that the elements are given by minimal linear representations. It relies…
In order to design strong paradigms for isolating lexical access and semantics, we need to know what a word is. Surprisingly few linguists and philosophers have a clear model of what a word is, even though words impact basically every…
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
The fundamentals of formal logic, theory of sets and mathematical structures are narrated in terms of relations language.
In the talk at the workshop my aim was to demonstrate the usefulness of graph techniques for tackling problems that have been studied predominantly as problems on the term level: increasing sharing in functional programs, and addressing…
We introduce a meta-model based on formal languages, dubbed formal choreographic languages, to study message-passing systems. Our framework allows us to generalise standard constructions from the literature and to compare them. In…
We extend Borel's theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel's theorem to some words with constants. We also consider the surjectivity problem for…
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…
These informal notes deal with a number of questions related to sums and integrals in analysis.
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…