Related papers: On optimal Scott sentences of finitely generated a…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
In this paper, we determine the descriptive complexity of subsets of the Polish space of marked groups defined by various group theoretic properties. In particular, using Grigorchuk groups, we establish that the sets of solvable groups,…
For a finite word $w$ we define and study the Kolmogorov structure function $h_w$ for nondeterministic automatic complexity. We prove upper bounds on $h_w$ that appear to be quite sharp, based on numerical evidence.
We affirm a conjecture of Sacks [1972] by showing that every countable distributive lattice is isomorphic to an initial segment of the hyperdegrees, $\mathcal{D}_{h}$. In fact, we prove that every sublattice of any hyperarithmetic lattice…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
In this article, we show that the completion problem, i.e. the decision problem whether a partial structure can be completed to a full structure, is NP-complete for many combinatorial structures. While the gadgets for most reductions in…
We study the definability of maximal towers and of inextendible linearly ordered towers (ilt's), a notion that is more general than that of a maximal tower. We show that there is, in the constructible universe, a $\Pi^1_1$ definable maximal…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…
It is often stated that human languages, as other biological systems, are shaped by cost-cutting pressures but, to what extent? Attempts to quantify the degree of optimality of languages by means of an optimality score have been scarce and…
Given an arbitrary group $G$ we construct a semigroup of idempotents (band) $B_G$ with the property that the free idempotent generated semigroup over $B_G$ has a maximal subgroup isomorphic to $G$. If $G$ is finitely presented then $B_G$ is…
Constructive meaning is given to the assertion that every finite Boolean algebra is an injective object in the category of distributive lattices. To this end, we employ Scott's notion of entailment relation, in which context we describe…
We introduce a term algebra as a new formal specification language for the coordinating architectures of distributed systems consisting of a finite yet unbounded number of components. The language allows to describe infinite sets of systems…
Let $G$ be a finite group. We let $\f{m}(G)$ and $\sig(G)$ denote the number of maximal subgroups of $G$ and the least positive integer $n$ such that $G$ is written as the union of $n$ proper subgroups, respectively. In this paper we…
We show that the finiteness length of an $S$-arithmetic subgroup $\Gamma$ in a noncommutative isotropic absolutely almost simple group $G$ over a global function field is one less than the sum of the local ranks of $G$ taken over the places…
We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem…
For an arbitrary group, the subgroups form a lattice with order determined by set inclusion. Not every lattice is isomorphic to the subgroup lattice for a group. However, Birkhoff and Frink proved that any compactly generated lattice is…
We are interested in proving input-output properties of functions that handle infinite data such as streams or non-wellfounded trees. We provide a finitary refinement type system which is (sound and) complete for Scott-open properties…
This paper considers the computational hardness of computing expected outcomes and deciding (universal) (positive) almost-sure termination of probabilistic programs. It is shown that computing lower and upper bounds of expected outcomes is…
We discuss the definability of finite graphs in first-order logic with two relation symbols for adjacency and equality of vertices. The logical depth $D(G)$ of a graph $G$ is equal to the minimum quantifier depth of a sentence defining $G$…