Formal Languages and Automata Theory
In this work, we introduce a new notion for representing graph classes with formal languages. In contrast to the seminal work by Kitaev and Pyatkin to represent graphs by words, we use formal binary languages in order to have a set of…
We study the most elementary family of cellular automata defined over an arbitrary group universe $G$ and an alphabet $A$: the lazy cellular automata, which act as the identity on configurations in $A^G$, except when they read a unique…
We introduce weighted finite finance automata (WFFA), a formal framework for modeling and analyzing quantitative properties of financial systems driven by uncertain economic variables such as stock prices, interest rates, and exchange…
Classical automata theory is far more capable of modeling complex digital systems than is widely acknowledged in the ``formal methods'' literature. This paper takes a second look at automata theory methods that were mostly developed in the…
Embeddings of word structures into matrix semigroups provide a natural bridge between combinatorics on words and linear algebra. However, low-dimensional matrix semigroups impose strong structural restrictions on possible embeddings.…
For a fixed alphabet A, an infinite sequence X is said to be normal if every word w over A appears in X with the same frequency as any other word of the same length. A classical result relates normality to finite automata as follows: a…
We present a Myhill-Nerode style characterization for languages recognized by one-clock deterministic timed automata (1-DTA). Although there is only one clock, distinct automata may reset it differently along the same word. This adds a…
This paper addresses the lifting problem for the \v{C}ern\'y conjecture: namely, whether the validity of the conjecture for a quotient automaton can always be transferred (or "lifted") to the original automaton. Although a complete solution…
In this work, we study minimization of rational functions given as appending streaming string transducers (aSST for short). We rely on an algebraic presentation of these functions, known as bimachines, to address the minimization of both…
This is an extended version of our publication Learning state machines from data streams: A generic strategy and an improved heuristic, International Conference on Grammatical Inference (ICGI) 2023, Rabat, Morocco. It has been extended with…
We present a novel perspective on the NFA canonization problem, which introduces intermediate minimization steps to reduce the exploration space on-the-fly. Central to our approach are equivalence registries which track and unify…
A product of Moore machines with feedback published in 1962 by Juris Hartmanis and a class of primitive recursive functions on finite sequences published in a textbook by Roza Peter originally in 1950 are keys to a method for working with…
Generalized finite automata (GFAs), probabilistic finite automata (PFAs), and one-way general quantum finite automata (1gQFA) recognize the same strict-cutpoint languages, but the state complexity of exact probabilistic simulation has…
Active automata learning (AAL) under a Minimally Adequate Teacher (MAT) has been successfully used to infer a regular language through membership and equivalence queries. This language might not be fully characterized: we are then…
We propose a scalable framework for deciding, proving, and explaining (in-)equivalence of context-free grammars. We present an implementation of the framework and evaluate it on large data sets collected within educational support systems.…
This paper presents a set of algorithms for computing the reachability graph of Petri Net Product Lines (PNPLs). These algorithms address the combined challenges of concurrency and variability that arise from product-line configurations.…
We study decision problems of the form: given a regular or linear context-free language $L$, is there a word of a given fixed form in $L$, where given fixed forms are based on word operations copy, marked copy, shuffle and their…
A morphism $g$ from the free monoid $X^*$ into itself is called upper triangular if the matrix of $g$ is upper triangular. We characterize all upper triangular binary morphisms $g_1$ and $g_2$ such that $g_1g_2=g_2g_1$.
The state complexity, respectively, nondeterministic state complexity of a regular language $L$ is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for $L$. Some of the most…
A model of an information system describes its processes and how resources are involved in these processes to manipulate data objects. This paper presents an extension to the Petri nets formalism suitable for describing information systems…