形式语言与自动机理论

We prove that a random automaton with $n$ states and any fixed non-singleton alphabet is synchronizing with high probability (modulo an unpublished result about unique highest trees of random graphs). Moreover, we also prove that the…

We introduce and study a generalized Parikh matrix mapping based on tracking the occurrence counts of special types of subsequences. These matrices retain more information about a word than the original Parikh matrix mapping while…

We study weighted basic parallel processes (WBPP), a nonlinear recursive generalisation of weighted finite automata inspired from process algebra and Petri net theory. Our main result is an algorithm of 2-EXPSPACE complexity for the WBPP…

We present a system for Complex Event Recognition (CER) based on automata. While multiple such systems have been described in the literature, they typically suffer from a lack of clear and denotational semantics, a limitation which often…

This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…

We consider a class of finite state three-tape transducers which models the operation of shuffling and splitting words. We present them as automata over the so-called Shuffling Monoid. These automata can be seen as either shufflers or…

We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…

Weighted automata (WA) are an extension of finite automata that define functions from words to values in a given semiring. An alternative deterministic model, called Cost Register Automata (CRA), was introduced by Alur et al. It enriches…

A labelled Markov decision process (MDP) is a labelled Markov chain with nondeterminism; i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by…

Probabilistic deterministic finite automata (PDFA) are discrete event systems modeling conditional probabilities over languages: Given an already seen sequence of tokens they return the probability of tokens of interest to appear next.…

Deterministic two-way transducers capture the class of regular functions. The efficiency of composing two-way transducers has a direct implication in algorithmic problems related to reactive synthesis, where transformation specifications…

In 2021, Casares, Colcombet and Fijalkow introduced the Alternating Cycle Decomposition (ACD), a structure used to define optimal transformations of Muller into parity automata and to obtain theoretical results about the possibility of…

We investigate the transition monoid construction for deterministic automata in a categorical setting and establish it as an adjunction. We pair this adjunction with two other adjunctions to obtain two endofunctors on deterministic…

This thesis studies the single-use restriction for register automata and transducers over infinite alphabets. The restriction requires that a read-access to a register should have the side effect of destroying its contents. This constraint…

Backreference is a well-known practical extension of regular expressions and most modern programming languages, such as Java, Python, JavaScript and more, support regular expressions with backreferences (rewb) in their standard libraries…

In order to ensure autonomous vehicles are safe for on-road deployment, simulation-based testing has become an integral complement to on-road testing. The rise in simulation testing and validation reflects a growing need to verify that AV…

In the present work, we exhibit a class of self-descriptive sequences that can be explicitly computed and whose frequencies are known. In particular, as a corollary of our main result, we prove that the sequence introduced in \citeBJM23 has…

We introduce global one-counter tree automata (GOCTA) which deviate from usual counter tree automata by working on only one counter which is passed through the tree in lexicographical order, rather than duplicating the counter at every…

The bandwidth of timed automata characterizes the quantity of information produced/transmitted per time unit. We previously delimited 3 classes of TA according to the nature of their asymptotic bandwidth: meager, normal, and obese. In this…

Information-flow interfaces is a formalism recently proposed for specifying, composing, and refining system-wide security requirements. In this work, we show how the widely used concept of security lattices provides a natural semantic…