相关论文: An Explicit Solution to Post's Problem over the Re…

The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…

Writing correct distributed programs is hard. In spite of extensive testing and debugging, software faults persist even in commercial grade software. Many distributed systems, especially those employed in safety-critical environments,…

This paper concerns the tilt stability of local optimal solutions to a class of nonlinear semidefinite programs, which involves a twice continuously differentiable objective function and a convex feasible set. By leveraging the second…

The past decade has seen a significant interest in learning tractable probabilistic representations. Arithmetic circuits (ACs) were among the first proposed tractable representations, with some subsequent representations being instances of…

In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…

We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…

Lower bounds for some explicit decision problems over the complex numbers are given.

Language models often generate reasoning before giving a final answer, but the visible answer does not reveal when the model's answer preference became stable. We study this question through a narrow computable object: \emph{finite-answer…

A generic computation of a subset $A$ of $\mathbb{N}$ is a computation which correctly computes most of the bits of $A$, but which potentially does not halt on all inputs. The motivation for this concept is derived from complexity theory,…

Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual…

We study the problem of regular separability of languages of vector addition systems with states (VASS). It asks whether for two given VASS languages K and L, there exists a regular language R that includes K and is disjoint from L. While…

We present a new asynchronous model of computation named Stellar Resolution based on first-order unification. This model of computation is obtained as a formalisation of Girard's transcendental syntax programme, sketched in a series of…

We show that all--instances termination of chase is undecidable. More precisely, there is no algorithm deciding, for a given set $\cal T$ consisting of Tuple Generating Dependencies (a.k.a. Datalog$^\exists$ program), whether the $\cal…

We provide a logical characterization of non-deterministic polynomial time defined by BSS machines over semirings via existential second-order logic interpreted in the semiring semantics developed by Gr\"adel and Tannen. Furthermore, we…

In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…

Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…

The fixed-template constraint satisfaction problem (CSP) can be seen as the problem of deciding whether a given primitive positive first-order sentence is true in a fixed structure (also called model). We study a class of problems that…

Fact-checking real-world claims, particularly numerical claims, is inherently complex that require multistep reasoning and numerical reasoning for verifying diverse aspects of the claim. Although large language models (LLMs) including…

We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…

Counterfactual explanations (CEs) offer a human-understandable way to explain decisions by identifying specific changes to the input parameters of a base or present model that would lead to a desired change in the outcome. For optimization…