Related papers: Randomized Distributed Decision
A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
It is a widely believed, though unproven, conjecture that the capability of postselection increases the language recognition power of both probabilistic and quantum polynomial-time computers. It is also unknown whether polynomial-time…
Large Language Models (LLMs) have transformed text generation through inherently probabilistic context-aware mechanisms, mimicking human natural language. In this paper, we systematically investigate the performance of various LLMs when…
Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the…
We introduce probabilistic language tries (PLTs), a unified representation that makes explicit the prefix structure implicitly defined by any generative model over sequences. By assigning to each outgoing edge the conditional probability of…
In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
One of the cornerstones of the distributed complexity theory is the derandomization result by Chang, Kopelowitz, and Pettie [FOCS 2016]: any randomized LOCAL algorithm that solves a locally checkable labeling problem (LCL) can be…
In this paper, we extend the techniques used in our previous work to show that there exists a probabilistic Turing machine running within time $O(n^k)$ for all $k\in\mathbb{N}_1$ accepting a language $L_d$ that is different from any…
In Probabilistic Logic Nilsson uses the device of a probability distribution over a set of possible worlds to assign probabilities to the sentences of a logical language. In his paper Nilsson concentrated on inference and associated…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
This paper contains an extensive combinatorial analysis of the single-peaked domain restriction and investigates the likelihood that an election is single-peaked. We provide a very general upper bound result for domain restrictions that can…
Large language models (LLMs) have shown to be increasingly capable of performing reasoning tasks, but their ability to make sequential decisions under uncertainty only using natural language remains underexplored. We introduce a novel…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
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…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
The aim of this thesis is to determine classes of NP relations for which random generation and approximate counting problems admit an efficient solution. Since efficient rank implies efficient random generation, we first investigate some…