Related papers: Intrinsic Sequentiality in P: Causal Limits of Par…
We study the complexity of a class of problems involving satisfying constraints which remain the same under translations in one or more spatial directions. In this paper, we show hardness of a classical tiling problem on an N x N…
One way to study the physical plausibility of closed timelike curves (CTCs) is to examine their computational power. This has been done for Deutschian CTCs (D-CTCs) and post-selection CTCs (P-CTCs), with the result that they allow for the…
Chain of thought is a natural inference-time method for increasing the computational power of transformer-based large language models (LLMs), but comes at the cost of sequential decoding. Are there more efficient alternatives to expand a…
It is well known that the kind of P systems involved in the definition of the P conjecture is able to solve problems in the complexity class $\mathbf{P}$ by leveraging the uniformity condition. Here we show that these systems are indeed…
Real-time systems increasingly use multicore processors in order to satisfy thermal, power, and computational requirements. To exploit the architectural parallelism offered by the multicore processors, parallel task models, scheduling…
Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs,…
While prior work established a verifier-based polynomial-time framework for NP, explicit deterministic machines for concrete NP-complete problems have remained elusive. In this paper, we construct fully specified deterministic Turing…
In this paper we study flow problems on temporal networks, where edge capacities and travel times change over time. We consider a network with $n$ nodes and $m$ edges where the capacity and length of each edge is a piecewise constant…
This paper solves a long standing open problem of whether NP-complete problems could be solved in polynomial time on a deterministic Turing machine by showing that the indistinguishable binomial decision tree can be formed in a 3-SAT…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
We study the deterministic complexity of the $2$-Ruling Set problem in the model of Massively Parallel Computation (MPC) with linear and strongly sublinear local memory. Linear MPC: We present a constant-round deterministic algorithm for…
Causal consistency is one of the most adopted consistency criteria for distributed implementations of data structures. It ensures that operations are executed at all sites according to their causal precedence. We address the issue of…
This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
We study the possibility of designing $N^{o(1)}$-round protocols for problems of substantially super-linear polynomial-time (sequential) complexity on the congested clique with about $N^{1/2}$ nodes, where $N$ is the input size. We show…
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…
The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…
We present a parallel scan (prefix sum) algorithm in the Tensor Core Unit (TCU) model of computation. The TCU model assumes that multiplication between two square matrices of constant size $s$ is a basic operation. In the $(s^2, \ell)$-TCU…
This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization of the complexity blowup for a class of ODEs of arbitrary…
We investigate the global scheduling of sporadic, implicit deadline, real-time task systems on multiprocessor platforms. We provide a task model which integrates job parallelism. We prove that the time-complexity of the feasibility problem…
Time-series causal discovery (TSCD) is a fundamental problem of machine learning. However, existing synthetic datasets cannot properly evaluate or predict the algorithms' performance on real data. This study introduces the CausalTime…