相关论文: Unsolvability Cores in Classification Problems

Causal probing aims to analyze foundation models by examining how intervening on their representation of various latent properties impacts their outputs. Recent works have cast doubt on the theoretical basis of several leading causal…

Recently, the separated fragment (SF) has been introduced and proved to be decidable. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. The known upper bound on the time…

Rice's theorem shows that nontrivial extensional properties of partial recursive functions are undecidable. For finite weighted Boolean optimization/CSP-style slices, a Rice-style structural analogue holds for tractability classification:…

The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures.…

We consider the new extension of population protocols with unordered data and show that the corresponding well-specification problem and therefore also other verification problems are undecidable.

Two types of explanations have been receiving increased attention in the literature when analyzing the decisions made by classifiers. The first type explains why a decision was made and is known as a sufficient reason for the decision, also…

We investigate replicable learning algorithms. Ideally, we would like to design algorithms that output the same canonical model over multiple runs, even when different runs observe a different set of samples from the unknown data…

For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…

We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…

We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…

Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

The $P$ versus $NP$ problem is still unsolved. But there are several oracles with $P$ unequal $NP$ relative to them. Here we will prove, that $P\not=NP$ relative to a $P$-complete oracle. In this paper, we use padding arguments as the proof…

In the interleaving model of concurrency, where events are totally ordered, linearizability is compositional: the composition of two linearizable objects is guaranteed to be linearizable. However, linearizability is not compositional when…

First-order logic, and quantifiers in particular, are widely used in deductive verification. Quantifiers are essential for describing systems with unbounded domains, but prove difficult for automated solvers. Significant effort has been…

We consider the problem of whether a given decision model, working with structured data, has individual fairness. Following the work of Dwork, a model is individually biased (or unfair) if there is a pair of valid inputs which are close to…

In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…

We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…

The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of…

Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…