Related papers: Asynchronous Distributed Automata: A Characterizat…
Synchronous computation models simplify the design and the verification of fault-tolerant distributed systems. For efficiency reasons such systems are designed and implemented using an asynchronous semantics. In this paper, we bridge the…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
We define compact automata and show that every language has a unique minimal compact automaton. We also define recognition of languages by compact left semitopological monoids and construct the analogue of the syntactic monoid in this…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and St\"ark for reasoning about hierarchical…
Characterisations theorems serve as important tools in model theory and can be used to assess and compare the expressive power of temporal languages used for the specification and verification of properties in formal methods. While complete…
We consider a solution of automata similar to Population Protocols and Network Constructors. The automata (or nodes) move passively in a well-mixed solution and can cooperate by interacting in pairs. Every such interaction may result in an…
We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make…
Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular verification problems. In this paper, we consider a generalization…
Our main contributions can be divided in three parts: (1) Fixpoint extensions of first-order logic: we give a precise syntactic and semantic characterization of the relationship between $\mathrm{FO(TC^1)}$ and $\mathrm{FO(LFP)}$; (2)…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
Temporal graphs represent graph evolution over time, and have been receiving considerable research attention. Work on expressing temporal graph patterns or discovering temporal motifs typically assumes relatively simple temporal…
The topological and metrical equivalence of fractals is an important topic in analysis. In this paper, we use a class of finite state automata, called $\Sigma$-automaton, to construct psuedo-metric spaces, and then apply them to the study…
The immediate past has witnessed an increased amount of interest in local algorithms, i.e., constant time distributed algorithms. In a recent survey of the topic (Suomela, ACM Computing Surveys, 2013), it is argued that local algorithms…
We investigate the conditions under which the mean-field formulation of a probabilistic, totalistic cellular automaton approximates the logistic equation. We show that this goal can be only fulfilled for an infinite-range neighborhood. We…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…