Related papers: Solution sets for equations over free groups are E…
In this paper, we consider block languages, namely sets of words having the same length, and we propose a new representation for these languages. In particular, given an alphabet of size $k$ and a length $\ell$, a block language can be…
Most state-of-the-art approaches for named-entity recognition (NER) use semi supervised information in the form of word clusters and lexicons. Recently neural network-based language models have been explored, as they as a byproduct generate…
Lists of equivalence classes of words under rotation or rotation plus reversal (i.e., necklaces and bracelets) have many uses, and efficient algorithms for generating these lists exist. In combinatorial group theory elements of a group are…
Datalog is a popular logic programming language for deductive reasoning tasks in a wide array of applications, including business analytics, program analysis, and ontological reasoning. However, Datalog's restriction to flat facts over…
The category of all idempotent generated semigroups with a prescribed structure $\mathcal{E}$ of their idempotents $E$ (called the biordered set) has an initial object called the free idempotent generated semigroup over $\mathcal{E}$,…
We develop and explore the idea of recognition of languages (in the general sense of subsets of topological algebras) as preimages of clopen sets under continuous homomorphisms into Stone topological algebras. We obtain an Eilenberg…
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…
We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We consider the case where the code-related property is…
A finitary propositional logic can be given an algebraic reading in two different ways: by translating formulas into equations and logical rules into quasi-equations, or by translating logical rules directly into equations. The former type…
Recent years have witnessed the success of dictionary learning (DL) based approaches in the domain of pattern classification. In this paper, we present an efficient structured dictionary learning (ESDL) method which takes both the diversity…
We introduce a new notion of C-simple problems for a class C of decision problems (i.e. languages), w.r.t. a particular reduction. A problem is C-simple if it can be reduced to each problem in C. This can be viewed as a conceptual…
One of the key steps in the proof of the Banach-Tarski Theorem is the introduction of a free group of rotations. First, a free group of reduced words is generated where each element of the set is represented as an ACL2 list. Then we…
We investigate in a method for proving separation results for abstract classes of languages. A well established method to characterize varieties of regular languages are identities. We use a recently established generalization of these…
The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups as well as the set of all solutions of equations in free monoids…
Derivative-free optimization (DFO) consists in finding the best value of an objective function without relying on derivatives. To tackle such problems, one may build approximate derivatives, using for instance finite-difference estimates.…
William W. Boone and Graham Higman proved that a finitely generated group has soluble word problem if and only if it can be embedded in a simple group that can be embedded in a finitely presented group. We prove the exact analogue for…
This paper contributes to a theory of the behaviour of "finite-state" systems that is generic in the system type. We propose that such systems are modelled as coalgebras with a finitely generated carrier for an endofunctor on a locally…
This paper is concerned with a class of algorithms that perform exhaustive search on propositional knowledge bases. We show that each of these algorithms defines and generates a propositional language. Specifically, we show that the trace…
An involution on a finite set is a bijection such as I(I(e))=e for all the element of the set. A fixed-point free involution on a finite set is an involution such as I(e)=e for none element of the set. In this article, the fixed-point free…
We consider the set of infinite real traces, over a dependence alphabet (Gamma, D) with no isolated letter, equipped with the topology induced by the prefix metric. We then prove that all rational languages of infinite real traces are…