相关论文: On deterministic, constant memory triangular searc…
We consider the problem of finding a treasure at an unknown point of an $n$-dimensional infinite grid, $n\geq 3$, by initially collocated finite state agents (scouts/robots). Recently, the problem has been well characterized for 2…
Consider a group of autonomous mobile computational entities, called agents, arbitrarily placed at some nodes of a dynamic but always connected ring. The agents neither have any knowledge about the size of the ring nor have a common notion…
We study the problem of online tree exploration by a deterministic mobile agent. Our main objective is to establish what features of the model of the mobile agent and the environment allow linear exploration time. We study agents that, upon…
We study the problem of deterministically exploring an undirected and initially unknown graph with $n$ vertices either by a single agent equipped with a set of pebbles, or by a set of collaborating agents. The vertices of the graph are…
A mobile agent equipped with a compass and a measure of length has to find an inert treasure in the Euclidean plane. Both the agent and the treasure are modeled as points. In the beginning, the agent is at a distance at most $D>0$ from the…
We introduce a differentiable random access memory module with $O(1)$ performance regardless of size, scaling to billions of entries. The design stores entries on points of a chosen lattice to calculate nearest neighbours of arbitrary…
In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all…
The problem of electing a unique leader is central to all distributed systems, including programmable matter systems where particles have constant size memory. In this paper, we present a silent self-stabilising, deterministic, stationary,…
We study the problem of exploring an oriented grid with autonomous agents governed by finite automata. In the case of a 2-dimensional grid, the question how many agents are required to explore the grid, or equivalently, find a hidden…
The nearest lattice point problem in $\mathbb{R}^n$ is formulated in a distributed network with $n$ nodes. The objective is to minimize the probability that an incorrect lattice point is found, subject to a constraint on inter-node…
In a rendezvous task, some mobile agents dispersed in a network have to gather at an arbitrary common site. We consider the rendezvous problem on the infinite labeled line, with $2$ agents, without communication, and a synchronous notion of…
Many recent long-context and agentic systems address context-length limitations by adding hierarchical memory: they extract atomic units from raw data, build multi-level representatives by grouping and compression, and traverse this…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. The…
A deterministic algorithm for factoring $n$ using $n^{1/3+o(1)}$ bit operations is presented. The algorithm tests the divisibility of $n$ by all the integers in a short interval at once, rather than integer by integer as in trial division.…
We study the problem of enumerating Tarski fixed points on finite lattices. We derive query complexity lower bounds for finding three or more Tarski fixed points of isotone maps and the subclasses of increasing and decreasing isotone maps.…
The importance of classifying connections in large graphs has been the motivation for a rich line of work on distributed subgraph finding that has led to exciting recent breakthroughs. A crucial aspect that remained open was whether…
A mobile agent has to find an inert target in some environment that can be a graph or a terrain in the plane. This task is known as treasure hunt. We consider deterministic algorithms for treasure hunt in trees. Our goal is to establish the…
Large Language Models (LLMs) have demonstrated remarkable emergent capabilities, yet the robustness of their numerical reasoning remains an open question. While standard benchmarks evaluate LLM reasoning on complex problem sets using…
Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms…
Two mobile agents, starting at arbitrary, possibly different times from arbitrary nodes of an unknown network, have to meet at some node. Agents move in synchronous rounds: in each round an agent can either stay at the current node or move…