Related papers: Synchronization of primitive automata
It is known, that an $\epsilon$-machine is either exactly or asymptotically synchronizing. In the exact case, the observer can infer the current machine state after observing $L$ generated symbols with probability $1-a^L$ where $0 \leq a<1$…
Symbolic Finite Automata and Register Automata are two orthogonal extensions of finite automata motivated by real-world problems where data may have unbounded domains. These automata address a demand for a model over large or infinite…
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…
We present a necessary and sufficient condition for a random product of maps on a compact metric space to be (strongly) synchronizing on average.
We revisit the problem of synchronisability for communicating automata, i.e., whether the language of send messages for an asynchronous system is the same as the language of send messages with a synchronous communication. The…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
A nonnegative matrix $A$ is called primitive if $A^k$ is positive for some integer $k>0$. A generalization of this concept to finite sets of matrices is as follows: a set of matrices $\mathcal M = \{A_1, A_2, \ldots, A_m \}$ is primitive if…
A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. Jan Cerny had found in 1964 a sequence of n-state complete DFA with…
Linearizability is the de facto consistency condition for concurrent objects, widely used in theory and practice. Loosely speaking, linearizability classifies concurrent executions as correct if operations on shared objects appear to take…
We study qualitative properties of two-dimensional freezing cellular automata with a binary state set initialized on a random configuration. If the automaton is also monotone, the setting is equivalent to bootstrap percolation. We explore…
We describe the methods and results of a classification of the non-synchronizing primitive permutation groups of degree up to 624. We make use of theory and computation to determine the primitive groups of degree up to 624 that are…
The automaticity $A(x)$ of a set $\mathcal{X}$ is the size of the smallest automaton that recognizes $\mathcal{X}$ on all words of length $\leq x$. We show that the automaticity of the set of primes is at least $x\exp\left(-c(\log\log…
To translate speech for automatic dubbing, machine translation needs to be isochronous, i.e. translated speech needs to be aligned with the source in terms of speech durations. We introduce target factors in a transformer model to predict…
We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this…
Given a right-infinite word $\bf x$ over a finite alphabet $A$, the rank of $\bf x$ is the size of the smallest set $S$ of words over $A$ such that $\bf x$ can be realized as an infinite concatenation of words in $S$. We show that the…
Synchronous programming languages emerged in the 1980s as tools for implementing reactive systems, which interact with events from physical environments and often must do so under strict timing constraints. In this report, we encode inside…
Imitation learning in robots, also called programing by demonstration, has made important advances in recent years, allowing humans to teach context dependant motor skills/tasks to robots. We propose to extend the usual contexts…
We study interacting components and their compatibility with respect to synchronous and asynchronous composition. The behavior of components is formalized by I/O-transition systems. Synchronous composition is based on simultaneous execution…
We use the notion of a partial action of a monoid to introduce a generalization of automata, which we call "a preautomaton". We study properties of preautomata and of languages recognized by preautomata.
In this paper we introduce a new type of approximate state reductions where the behaviors of the reduced and the original automaton do not have to be identical, but they must match on all words of length less than or equal to some given…