Related papers: Decidability of Interpretability
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
The classifications of temporal and phylogeny constraint languages stand among the most seminal complexity classifications within infinite-domain Constraint Satisfaction Problems (CSPs), yet remain the most mysterious in terms of algorithms…
The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
We study comparisons between interpretations in description logics with respect to "logical consequences" of the form of semi-positive concepts (like semi-positive concept assertions). Such comparisons are characterized by conditions…
We investigate different notions of "computable topological base" for represented spaces. We show that several non-equivalent notions of bases become equivalent when we consider computably enumerable bases. This indicates the existence of a…
The Constraint Satisfaction Problem (CSP) is a problem of computing a homomorphism $\mathbf{R}\to \mathbf{\Gamma}$ between two relational structures, where $\mathbf{R}$ is defined over a domain $V$ and $\mathbf{\Gamma}$ is defined over a…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
The universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two…
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…
Constraint satisfaction problems (CSPs) are a natural class of decision problems where one must decide whether there is an assignment to variables that satisfies a given formula. Schaefer's dichotomy theorem, and its extension to all…
This paper aims at developing model-theoretic tools to study interpretable fields and definably amenable groups, mainly in $\mathrm{NIP}$ or $\mathrm{NTP_2}$ settings. An abstract theorem constructing definable group homomorphisms from…
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…
Brouwer's constructivist foundations of mathematics is based on an intuitively meaningful notion of computation shared by all mathematicians. Martin-L\"of's meaning explanations for constructive type theory define the concept of a type in…
Quasi-interpretations are a technique to guarantee complexity bounds on first-order functional programs: with termination orderings they give in particular a sufficient condition for a program to be executable in polynomial time, called…
We analyze the effective content of countable, second countable topological spaces by directly calculating the complexity of several topologically defined index sets. We focus on the separation principles, calibrating an arithmetic…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
Friedman and Stanley developed the notion of Borel reducibility and illustrated its use in comparing classification problems for some familiar classes of countable structures. For many embeddings, the fact that the embedding is $1-1$ on…
The Chinese Remainder Theorem for the integers says that every system of congruence equations is solvable as long as the system satisfies an obvious necessary condition. This statement can be generalized in a natural way to arbitrary…
In this paper we study the complexity of counting Constraint Satisfaction Problems (CSPs) of the form #CSP($\mathcal{C}$,-), in which the goal is, given a relational structure $\mathbf{A}$ from a class $\mathcal{C}$ of structures and an…
We study a new notion of reduction between structures called enumerable functors related to the recently investigated notion of computable functors. Our main result shows that enumerable functors and effective interpretability with the…