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A finite automaton is called bideterministic if it is both deterministic and codeterministic -- that is, if it is deterministic and its transpose is deterministic as well. The study of such automata in a weighted setting is initiated. All…
In a \emph{separability problem}, we are given two sets $K$ and $L$ from a class $\mathcal{C}$, and we want to decide whether there exists a set $S$ from a class $\mathcal{S}$ such that $K\subseteq S$ and $S\cap L=\emptyset$. In this case,…
Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…
We classify the sets of natural numbers $n$ for which certain dynamical systems $(X,f)$ on a compact metric space $X$ have a periodic point of (least) period $n$. Interest in this question dates back to Sharkovskii's theorem for continuous…
Given a regular language L over an ordered alphabet $\Sigma$, the set of lexicographically smallest (resp., largest) words of each length is itself regular. Moreover, there exists an unambiguous finite-state transducer that, on a given word…
First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…
The states of a deterministic finite automaton A can be identified with collections of words in Pf(L(A)) -- the set of prefixes of words belonging to the regular language accepted by A. But words can be ordered and among the many possible…
We study three levels in a hierarchy of nondeterminism: A nondeterministic automaton $\mathcal{A}$ is determinizable by pruning (DBP) if we can obtain a deterministic automaton equivalent to $\mathcal{A}$ by removing some of its…
We propose a query learning algorithm for residual symbolic finite automata (RSFAs). Symbolic finite automata (SFAs) are finite automata whose transitions are labeled by predicates over a Boolean algebra, in which a big collection of…
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser's distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet $\Sigma$ of at least two elements, we…
In general, the representation of combinatorial objects is decisive for the feasibility of several enumerative tasks. In this work, we show how a (unique) string representation for (complete) initially-connected deterministic automata…
Bounded treewidth and Monadic Second Order (MSO) logic have proved to be key concepts in establishing fixed-parameter tractability results. Indeed, by Courcelle's Theorem we know: Any property of finite structures, which is expressible by…
The dot-depth hierarchy of Brzozowski and Cohen classifies the star-free languages of finite words. By a theorem of McNaughton and Papert, these are also the first-order definable languages. The dot-depth rose to prominence following the…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
We describe a simple algorithm which, for a given D0L system, returns all factors $v$ such that $v^k$ is in the language of the system for all $k$. This algorithm can be used to decide whether a D0L system is repetitive.
The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…
Algorithms are developed for the quickest detection of a change in statistically periodic processes. These are processes in which the statistical properties are nonstationary but repeat after a fixed time interval. It is assumed that the…
We consider the problem of learning a non-deterministic probabilistic system consistent with a given finite set of positive and negative tree samples. Consistency is defined with respect to strong simulation conformance. We propose learning…
A condition characterizing the class of regular languages which have several nonisomorphic minimal reversible automata is presented. The condition concerns the structure of the minimum automaton accepting the language under consideration.…
We show that the $n$'th digit of the base-$b$ representation of the golden ratio is a finite-state function of the Zeckendorf representation of $b^n$, and hence can be computed by a finite automaton. Similar results can be proven for any…