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We study the problem of finding connected components in the Adaptive Massively Parallel Computation (AMPC) model. We show that when we require the total space to be linear in the size of the input graph the problem can be solved in…
Artificial neural networks (ANNs) with recurrence and self-attention have been shown to be Turing-complete (TC). However, existing work has shown that these ANNs require multiple turns or unbounded computation time, even with unbounded…
The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through…
After an apparent hiatus of roughly 30 years, we revisit a seemingly neglected subject in the theory of (one-dimensional) cellular automata: sublinear-time computation. The model considered is that of ACAs, which are language acceptors…
The celebrated Time Hierarchy Theorem for Turing machines states, informally, that more problems can be solved given more time. The extent to which a time hierarchy-type theorem holds in the distributed LOCAL model has been open for many…
In this work, we investigate resource allocation strategy for real time communication (RTC) over satellite networks with virtual network functions. Enhanced by inter-satellite links (ISLs), in-orbit computing and network virtualization…
Inference-time scaling through multiple sample generation in combination with Process- or Outcome-Reward Model (PRM or ORM) re-ranking has proven effective for text-based reasoning in large language models. This paper investigates whether…
Data dissemination is a fundamental task in distributed computing. This paper studies broadcast problems in various innovative models where the communication network connecting $n$ processes is dynamic (e.g., due to mobility or failures)…
Test-time scaling is a promising new approach to language modeling that uses extra test-time compute to improve performance. Recently, OpenAI's o1 model showed this capability but did not publicly share its methodology, leading to many…
Despite significant advances, large language models (LLMs) continue to exhibit brittle performance on complex temporal reasoning tasks. This failure mode is widely attributed to inherent deficits in autoregressive logical deduction. In this…
Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…
The following two decision problems capture the complexity of comparing integers or rationals that are succinctly represented in product-of-exponentials notation, or equivalently, via arithmetic circuits using only multiplication and…
Test-time compute is central to large reasoning models, yet analysing their reasoning behaviour through generated text is increasingly impractical and unreliable. Response length is often used as a brute proxy for reasoning effort, but this…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
Scaling inference-time computation has substantially improved the reasoning capabilities of language models. However, existing methods have significant limitations: serialized chain-of-thought approaches generate overly long outputs,…
In this work, we develop the low-space Massively Parallel Computation (MPC) complexity landscape for a family of fundamental graph problems on trees. We present a general method that solves most locally checkable labeling (LCL) problems…
We give an exact algorithm for the 0-1 Integer Linear Programming problem with a linear number of constraints that improves over exhaustive search by an exponential factor. Specifically, our algorithm runs in time…
Independent component analysis (ICA) is the problem of efficiently recovering a matrix $A \in \mathbb{R}^{n\times n}$ from i.i.d. observations of $X=AS$ where $S \in \mathbb{R}^n$ is a random vector with mutually independent coordinates.…
For many years, Evolutionary Algorithms (EAs) have been applied to improve Neural Networks (NNs) architectures. They have been used for solving different problems, such as training the networks (adjusting the weights), designing network…
Connectivity in temporal graphs relies on the notion of temporal paths, in which edges follow a chronological order (either strict or non-strict). In this work, we investigate the question of how to make a temporal graph connected. More…