Related papers: Completely reducible sets
Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a $2$--complex -- the Squier complex -- whose fundamental groupoid then describes the…
We investigate complement-finite submonoids of the monoid of nonnegative integer points of a unipotent linear algebraic group $G$. These monoids are in general noncommutative but they specialize to the generalized numerical monoids of…
We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings,…
In this paper, we provide a new characterization of uniformly recurrent words with finite defect based on a relation between the palindromic and factor complexity. Furthermore, we introduce a class of morphisms P_ret closed under…
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…
The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category $\mathcal D$. This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the…
In this paper we prove several results regarding decidability of the membership problem for certain submonoids in amalgamated free products and HNN extensions of groups. These general results are then applied to solve the prefix membership…
We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…
We study the maximal subgroups (also known as group $\mathcal{H}$-classes) of finitely presented special inverse monoids. We show that the maximal subgroups which can arise in such monoids are exactly the recursively presented groups, and…
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…
We investigate the natural codings of linear involutions. We deduce from the geometric representation of linear involutions as Poincar\'e maps of measured foliations a suitable definition of return words which yields that the set of first…
We study arithmetic properties of factorizations of elements into products of generators, in monoids given with explicit presentations. After relating and comparing this perspective to the more usual approach of factoring into products of…
Reed-Muller codes belong to the family of affine-invariant codes. As such codes they have a defining set that determines them uniquely, and they are extensions of cyclic group codes. In this paper we identify those cyclic codes with…
We show that the Union-Closed Conjecture holds for the union-closed family generated by the cyclic translates of any fixed set.
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u)=\sum_{n=0}^{\infty} T(n) in which D(u) denotes the defect of u and T(n) denotes C(n+1)-C(n)+2-P(n+1)-P(n), where C…
In two previous papers we constructed new families of completely regular codes by concatenation methods. Here we determine cases in which the new codes are completely transitive. For these cases we also find the automorphism groups of such…
The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binary linear code are defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming…
We encode/decode Prolog terms as unique natural numbers. Our encodings have the following properties: a) are bijective b) natural numbers always decode to syntactically valid terms c) they work in low polynomial time in the bitsize of the…
We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments…