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We study the synthesis problem for systems with a parameterized number of processes. As in the classical case due to Church, the system selects actions depending on the program run so far, with the aim of fulfilling a given specification.…
LLM-driven web agents operating through continuous inference loops -- repeatedly querying a model to evaluate browser state and select actions -- exhibit a fundamental scalability constraint for repetitive tasks. We characterize this as the…
An automata network is a graph of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on the states…
Primary motivation for this work was the need to implement hardware accelerators for a newly proposed ANN structure called Auto Resonance Network (ARN) for robotic motion planning. ARN is an approximating feed-forward hierarchical and…
A linear arrangement (LA) is an assignment of distinct integers to the vertices of a graph. The cost of an LA is the sum of lengths of the edges of the graph, where the length of an edge is defined as the absolute value of the difference of…
Planning in public transportation is traditionally done in a sequential process: After the network design process, the lines and their frequencies are planned. When these are fixed, a timetable is determined and based on the timetable, the…
We investigate dynamic algorithms for the interval scheduling problem. Our algorithm runs in amortised time $O(\log n)$ for query operation and $O(d\log^2 n)$ for insertion and removal operations, where $n$ and $d$ are the maximal numbers…
Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a finite alphabet A. For these systems, we obtain a…
The sequential allocation protocol is a simple and popular mechanism to allocate indivisible goods, in which the agents take turns to pick the items according to a predefined sequence. While this protocol is not strategy-proof, it has been…
To implement a linearizable shared memory in synchronous message-passing systems it is necessary to wait for a time linear to the uncertainty in the latency of the network for both read and write operations. Waiting only for one of them…
We construct automata with input(s) in base $k$ recognizing some basic relations and study their number of states. We also consider some basic operations on $k$-automatic sequences $(h(i))_{i \geq 0}$ and discuss their state complexity. We…
Automata networks are a very general model of interacting entities, with applications to biological phenomena such as gene regulation. In many contexts, the order in which entities update their state is unknown, and the dynamics may be very…
An automata network is a network of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on states…
This paper studies the growing domain of Robotic Process Automation (RPA) problems. Motivated by scheduling problems arising in RPA, we study the parameterized complexity of the single-machine problem $1|\text{prec},r_j,d_j|*$. We focus on…
When we focus on finite dynamical systems from both the computability/complexity and the modelling standpoints, automata networks seem to be a particularly appropriate mathematical model on which theory shall be developed. In this paper,…
In this article, we study algorithms for dynamic networks with asynchronous start, i.e., each node may start running the algorithm in a different round. Inactive nodes transmit only heartbeats, which contain no information but can be…
Combinatorial optimization problems have wide-ranging applications in industry and academia. Quantum computers may help solve them by sampling from carefully prepared Ansatz quantum circuits. However, current quantum computers are limited…
We study the problem of scheduling jobs on fault-prone machines communicating via a shared channel, also known as multiple-access channel. We have $n$ arbitrary length jobs to be scheduled on $m$ identical machines, $f$ of which are prone…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
Most of the prior work in massively parallel data processing assumes homogeneity, i.e., every computing unit has the same computational capability, and can communicate with every other unit with the same latency and bandwidth. However, this…