Related papers: Synchronizing automata with random inputs
The synchronization between two dynamical systems is one of the most appealing phenomena occurring in Nature. Already observed by Huygens in the case of two pendula, it is a current area of research in the case of chaotic systems, with…
The state complexity of a Deterministic Finite-state automaton (DFA) is the number of states in its minimal equivalent DFA. We study the state complexity of random $n$-state DFAs over a $k$-symbol alphabet, drawn uniformly from the set…
In this work we use a framework of finite-state automata constructions based on equivalences over words to provide new insights on the relation between well-known methods for computing the minimal deterministic automaton of a language.
We construct a probabilistic finite automaton (PFA) with 7 states and an input alphabet of 5 symbols for which the PFA Emptiness Problem is undecidable. The only input for the decision problem is the starting distribution. For the proof, we…
This article studies the synchronization problem of complex dynamical networks. The impulsive control method is considered with a novel event-triggered pinning algorithm. Sufficient conditions on the network topology are obtained to ensure…
Parametric timed automata are a powerful formalism for reasoning on concurrent real-time systems with unknown or uncertain timing constants. Reducing their state space is a significant way to reduce the inherently large analysis times. We…
In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless…
An automaton is monotonic if its states can be arranged in a linear order that is preserved by the action of every letter. We prove that the problem of deciding whether a given automaton is monotonic is NP-complete. The same result is…
In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far…
In a generalized framework, where multi-state and inter-state linkages are allowed, we derive a sufficient condition for the stability of synchronization in a network of chaotic attractors. This condition explicitly relates the network…
There has been a growing interest in defining models of automata enriched with time, such as finite automata extended with clocks (timed automata). In this paper, we study deterministic timed finite state machines (TFSMs), i.e., finite…
When their reading heads are allowed to move completely asynchronously, finite-state automata with multiple tapes achieve a significant expressive power, but also lose useful closure properties---closure under intersection, in particular.…
This article focuses on subset reachability in synchronizing automata. First, we provide families of synchronizing automata with subsets which cannot be reached with short words. These families do not fulfil Don's Conjecture about subset…
We present a new series of examples of binary slowly synchronizing automata with sink state. The reset threshold of the $n$-state automaton in this series is $\frac{n^2}{4}+2n-9$. This improves on the previously known lower bound for the…
We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…
Timed automata are a convenient mathematical model for modelling and reasoning about real-time systems. While they provide a powerful way of representing timing aspects of such systems, timed automata assume arbitrary precision and…
When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct…
Sampled semantics of timed automata is a finite approximation of their dense time behavior. While the former is closer to the actual software or hardware systems with a fixed granularity of time, the abstract character of the latter makes…
We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions in order to have some form of almost sure asymptotic synchronization,…
We present the first study of non-deterministic weighted automata under probabilistic semantics. In this semantics words are random events, generated by a Markov chain, and functions computed by weighted automata are random variables. We…