Related papers: Synchronizing Random Almost-Group Automata
A quasi-automatic semigroup is defined by a finite set of generators, a rational (regular) set of representatives, such that if a is a generator or neutral, then the graph of right multiplication by a on the set of representatives is a…
A word w is called a synchronizing (recurrent, reset) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some state; a DFA that has a synchronizing word is said to be synchronizing. Cerny conjectured…
This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata…
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.…
Distributed automata are finite-state machines that operate on finite directed graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite…
In this paper we study the synchronization properties of random geometric graphs. We show that the onset of synchronization takes place roughly at the same value of the order parameter that a random graph with the same size and average…
Graph-walking automata (GWA) traverse graphs by moving between the nodes following the edges, using a finite-state control to decide where to go next. It is known that every GWA can be transformed to a GWA that halts on every input, to a…
We generalize the concept of synchronizing words for finite automata, which map all states of the automata to the same state, to deterministic visibly push-down automata. Here, a synchronizing word w does not only map all states to the same…
We apply a recently proposed dynamically driven renormalization group scheme to probabilistic cellular automata having one absorbing state. We have found just one unstable fixed point with one relevant direction. In the limit of small…
Limit-average automata are weighted automata on infinite words that use average to aggregate the weights seen in infinite runs. We study approximate learning problems for limit-average automata in two settings: passive and active. In the…
The {\em asynchronous automaton} associated with a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$, considered in many applications, is the finite deterministic automaton where the set of states is $\{0,1\}^n$, the alphabet is $[n]$, and the…
We generalize the partial derivative automaton to regular expressions with shuffle and study its size in the worst and in the average case. The number of states of the partial derivative automata is in the worst case at most 2^m, where m is…
A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. It was conjectured that in each completely…
This paper regards the relative localization problem in sensor networks. We study a randomized algorithm, which is based on input-driven consensus dynamics and involves pairwise "gossip" communications and updates. Due to the randomness of…
An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. The global dynamics of the network…
For a finite state automaton, a synchronizing sequence is an input sequence that takes all the states to the same state. Checking the existence of a synchronizing sequence and finding a synchronizing sequence, if one exists, can be…
We present a family of automata networks that solve the k-parity problem when run in parallel. These solutions are constructed by connecting cliques in a non-cyclical fashion. The size of the local neighbourhood is linear in the size of the…
We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the…
Planar automata seems to be representative of the synchronizing behavior of deterministic finite state automata. We conjecture that \v{C}erny's conjecture holds true, if and only if, it holds true for planar automata. In this paper we have…
An improved translation from alternating parity automata on infinite words to alternating weak automata is given. The blow-up of the number of states is related to the size of the smallest universal ordered trees and hence it is…