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We show that a special case of the Feferman-Vaught composition theorem gives rise to a natural notion of automata for finite words over an infinite alphabet, with good closure and decidability properties, as well as several logical…
We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that…
This paper studies linear stochastic approximation (SA) algorithms and their application to multi-agent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA…
We study the almost-sure reachability problem in a distributed system obtained as the asynchronous composition of N copies (called processes) of the same automaton (called protocol), that can communicate via a shared register with finite…
The question to enumerate all inclusion-minimal connected dominating sets in a graph of order $n$ in time significantly less than $2^n$ is an open question that was asked in many places. We answer this question affirmatively, by providing…
The existing algorithm to compute and verify the automata associated with an automatic group deals only with the subclass of shortlex automatic groups. This paper describes the extension of the algorithm to deal with automatic groups…
Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata…
Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of…
We study pushdown vector addition systems, which are synchronized products of pushdown automata with vector addition systems. The question of the boundedness of the reachability set for this model can be refined into two decision problems…
Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…
We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing…
We prove that a uniformly random automaton with $n$ states on a 2-letter alphabet has a synchronizing word of length $O(n^{1/2}\log n)$ with high probability (w.h.p.). That is to say, w.h.p. there exists a word $\omega$ of such length, and…
We present several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states. These automata are closely related to primitive digraphs with large exponent.
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
Using combinatorial properties of incomplete sets in a free monoid we construct a series of n-state deterministic automata with zero whose shortest synchronizing word has length n^2/4+n/2-1.
Timed pushdown automata (TPDA) are an expressive formalism combining recursion with a rich logic of timing constraints. We prove that reachability relations of TPDA are expressible in linear arithmetic, a rich logic generalising Presburger…
The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
This chapter is concerned with the design and analysis of algorithms for minimizing finite automata. Getting a minimal automaton is a fundamental issue in the use and implementation of finite automata tools in frameworks like text…
We consider decidability problems in self-similar semigroups, and in particular in semigroups of automatic transformations of $X^*$. We describe algorithms answering the word problem, and bound its complexity under some additional…