Related papers: Uniform decision problems and abstract properties …
We show that any finite monoid or semigroup presentation satisfying the small overlap condition C(4) has word problem which is a deterministic rational relation. It follows that the set of lexicographically minimal words forms a regular…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
We describe a practical algorithm for computing normal forms for semigroups and monoids with finite presentations satisfying so-called small overlap conditions. Small overlap conditions are natural conditions on the relations in a…
We show that being finitely presentable and being finitely presentable with solvable word problem are quasi-isometry invariants of finitely generated left cancellative monoids. Our main tool is an elementary, but useful, geometric…
We study the generic properties of finitely presented monoids and semigroups. We show that for positive integers a > 1, k and m, the generic a-generator k-relation monoid and semigroup presentation (defined in any of several definite…
A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show…
We show that, under suitable hypotheses, the coned-off spaces associated to $C(9)$ cubical small-cancellation presentations are aspherical, and use this to provide classifying spaces, or classifying spaces for proper actions, for their…
We show that under suitable hypotheses, the second homotopy group of the coned-off space associated to a $C(9)$ cubical presentation is trivial, and use this to provide classifying spaces for proper actions for the fundamental groups of…
We establish a new, fairly general cancellativity criterion for a presented monoid that properly extends the previously known related criteria. It is based on a new version of the word transformation called factor reversing, and its…
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…
It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To…
For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…
This article studies two notions of generalized matroid representations motivated by algorithmic information theory and cryptographic secret sharing. The first (entropic representability) involves discrete random variables, while the second…
In this paper we describe an algorithm for the computation of canonical forms of finite subsets of $\mathbb{Z}^d$, up to affinities over $\mathbb{Z}$. For fixed dimension $d$, this algorithm has worst-case asymptotic complexity $O(n \log^2…
We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…
We propose to use orthologic as the basis for designing type systems supporting intersection, union, and negation types in the presence of subtyping assumptions. We show how to extend orthologic to support monotonic and antimonotonic…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
We initiate the effective metric structure theory of Keisler randomizations. We show that a classical countable structure $\mathcal{M}$ has a decidable presentation if and only if its Borel randomization $\mathcal{M}^{[0,1)}$ has a…
We introduce cyclic diagram monoids, a generalisation of classical diagram monoids that adds elements of arbitrary period by including internal components, with a view towards cryptography. We classify their simple representations and…
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…