Formal Languages and Automata Theory
Given a deterministic finite automaton and its implementation with at most one single fault, that we can test on a set of inputs, we provide an algorithm to find a test set that guarantees finding whether the fault exists.
A minimal absent word of a sequence x, is a sequence yt hat is not a factorof x, but all of its proper factors are factors of x as well. The set of minimal absent words uniquely defines the sequence itself. In recent times minimal absent…
A two-dimensional string is simply a two-dimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs.…
We prove that for a given deterministic top-down transducer with look-ahead it is decidable whether or not its translation is definable (1)~by a linear top-down tree transducer or (2)~by a tree homomorphism. We present algorithms that…
In the \emph{Adapter Design Pattern}, a programmer implements a \emph{Target} interface by constructing an \emph{Adapter} that accesses an existing \emph{Adaptee} code. In this work, we present a reactive synthesis interpretation to the…
We implement a set of procedures for deciding whether or not a language given by its minimal automaton or by its syntactic semigroup is locally testable, right or left locally testable, threshold locally testable, strictly locally testable,…
Walnut is a software package that implements a mechanical decision procedure for deciding certain combinatorial properties of some special words referred to as automatic words or automatic sequences. Walnut is written in Java and is open…
Cyber Physical Systems (CPSs) are often black box systems for which no exact model exists. Automata learning allows to build abstract models of CPSs and is used in several scenarios, i.e. simulation, monitoring, and test case generation.…
A locally threshold testable language L is a language with the property that for some non negative integers k and l, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of length k > 1 and (2) the…
Universal register machine, a formal model of computation, can be emulated on the array of the Game of Life, a two-dimensional cellular automaton. We perform spectral analysis on the computation dynamical process of the universal register…
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…
In a recent paper E. Formenti and K. Perrot (FP) introduce a global rule assumed to describe the discrete time dynamics associated with a sandpile model under the parallel application of a suitable local rule acting on d dimensional…
We address the approximate minimization problem for weighted finite automata (WFAs) with weights in $\mathbb{R}$, over a one-letter alphabet: to compute the best possible approximation of a WFA given a bound on the number of states. This…
There are several proofs now for the stability of Toom's example of a two-dimensional stable cellular automaton and its application to fault-tolerant computation. Simon and Berman simplified and strengthened Toom's original proof: the…
Metric Temporal Logic can express temporally evolving properties with time-critical constraints or time-triggered constraints for real-time systems. This paper extends the Metric Interval Temporal Logic with a distribution eventuality…
We revisit here congruence relations for B\"uchi automata, which play a central role in the automata-based verification. The size of the classical congruence relation is in $3^{\mathcal{O}(n^2)}$, where $n$ is the number of states of a…
An efficient, when compared to exhaustive enumeration, algorithm for computing the number of square-free words of length $n$ over the alphabet $\{a, b, c\}$ is presented.
We study the synthesis of inductive half spaces (IHS). These are linear inequalities that form inductive invariants for Petri nets, capable of disproving reachability or coverability. IHS generalize classic notions of invariants like traps…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
We define a new quantitative measure for an arbitrary factorial language: the entropy of a random walk in the prefix tree associated with the language; we call it Markov entropy. We relate Markov entropy to the growth rate of the language…