Related papers: Recognizing Numbers
During the last decades, classical models in language theory have been extended by control mechanisms defined by monoids. We study which monoids cause the extensions of context-free grammars, finite automata, or finite state transducers to…
This paper deals with the problem of recognizability of functions l: Sigma* --> M that map words to values in the support set M of a monoid (M,.,1). These functions are called M-languages. M-languages are studied from the aspect of their…
Nominal sets provide a foundation for reasoning about names. They are used primarily in syntax with binders, but also, e.g., to model automata over infinite alphabets. In this paper, nominal sets are related to nominal renaming sets, which…
A countably infinite Boolean inverse monoid that can be written as an increasing union of finite Boolean inverse monoids (suitably embedded) is said to be of finite type. Borrowing terminology from $C^{\ast}$-algebra theory, we say that…
Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…
We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This…
In this paper, we assess the complexity results of formalisms that describe the feature theories used in computational linguistics. We show that from these complexity results no immediate conclusions can be drawn about the complexity of the…
We investigate a learning algorithm in the context of nominal automata, an extension of classical automata to alphabets featuring names. This class of automata captures nominal regular languages; analogously to the classical language…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
In algebraic terms, the insertion of $n$-powers in words may be modelled at the language level by considering the pseudovariety of ordered monoids defined by the inequality $1\le x^n$. We compare this pseudovariety with several other…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…
Inverse braid monoid describes a structure on braids where the number of strings is not fixed. So, some strings of initial $n$ may be deleted. In the paper we show that many properties and objects based on braid groups may be extended to…
Intelligent systems capable of automatically understanding natural language text are important for many artificial intelligence applications including mobile phone voice assistants, computer vision, and robotics. Understanding language…
Pomsets are a promising formalism for concurrent programs based on partially ordered sets. Among this class, series-parallel pomsets admit a convenient linear representation and can be recognized by simple algebraic structures known as…
We extend results from an earlier paper giving reconstruction results for the endomorphism monoid of the rational numbers under the strict and reflexive relations to the first order reducts of the rationals and the corresponding…
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…
We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Nonunique factorization in commutative monoids is often studied using factorization invariants, which assign to each monoid element a quantity determined by the factorization structure. For numerical monoids (co-finite, additive submonoids…
The aim of the paper is to build a connection between two approaches towards categorical language theory: the coalgebraic and algebraic language theory for monads. For a pair of monads modelling the branching and the linear type we defined…