Related papers: A Proof Checking View of Parameterized Complexity
Large language models (LLMs) are increasingly used in applications requiring factual accuracy, yet their outputs often contain hallucinated responses. While fact-checking can mitigate these errors, existing methods typically retrieve…
This paper presents a novel approach for augmenting proof-based verification with performance-style analysis of the kind employed in state-of-the-art model checking tools for probabilistic systems. Quantitative safety properties usually…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
In this paper, we evaluate the capability of transformer-based language models in making inferences over uncertain text that includes uncertain rules of reasoning. We cover both Pre-trained Language Models (PLMs) and generative Large…
We formally verify several computational reductions concerning the Post correspondence problem (PCP) using the proof assistant Coq. Our verifications include a reduction of a string rewriting problem generalising the halting problem for…
System development is not a linear, one-shot process. It proceeds through refinements and revisions. To support assurance that the system satisfies its requirements, it is desirable that continuous verification can be performed after each…
In this work, we develop new insights into the fundamental problem of convexity testing of real-valued functions over the domain $[n]$. Specifically, we present a nonadaptive algorithm that, given inputs $\eps \in (0,1), s \in \mathbb{N}$,…
A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a…
In purely functional programming languages imperative features, more generally computational effects are prohibited. However, non-functional lan- guages do involve effects. The theory of decorated logic provides a rigorous for- malism (with…
Neural models combining representation learning and reasoning in an end-to-end trainable manner are receiving increasing interest. However, their use is severely limited by their computational complexity, which renders them unusable on real…
We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
We examine a parameterized complexity class for randomized computation where only the error bound and not the full runtime is allowed to depend more than polynomially on the parameter, based on a proposal by Kwisthout in [15,16]. We prove…
Proof by coupling is a classical technique for proving properties about pairs of randomized algorithms by carefully relating (or coupling) two probabilistic executions. In this paper, we show how to automatically construct such proofs for…
Given a sound first-order p-time theory $T$ capable of formalizing syntax of first-order logic we define a p-time function $g_T$ that stretches all inputs by one bit and we use its properties to show that $T$ must be incomplete. We leave it…
We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
Quantum entanglement is a fundamental property of quantum mechanics and plays a crucial role in quantum computation and information. We study entanglement via the lens of computational complexity by considering quantum generalizations of…
In this article we introduce a new complexity class called PQMA_log(2). Informally, this is the class of languages for which membership has a logarithmic-size quantum proof with perfect completeness and soundness which is polynomially close…
Sorting is one of the most fundamental algorithms in computer science. Recently, Learned Sorts, which use machine learning to improve sorting speed, have attracted attention. While existing studies show that Learned Sort is empirically…