Related papers: Towards an algebraic characterization of rational …
The FAdo system is a symbolic manipulator of formal languages objects, implemented in Python. In this work, we extend its capabilities by implementing methods to manipulate transducers and we go one level higher than existing formal…
Higher-dimensional automata (HDA) are a model of concurrency that models simultaneous execution of events using higher dimensional cells. HDA recognize languages of pomsets, a generalization of finite words whose letters are partially…
Letter-to-letter transducers are a standard formalism for modeling reactive systems. Often, two transducers that model similar systems differ locally from one another, by behaving similarly, up to permutations of the input and output…
In this paper we develop little further the theory of quantum finite automata (QFA). There are already few properties of QFA known, that deterministic and probabilistic finite automata do not have e.g. they cannot recognize all regular…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…
Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is…
Counter machines have achieved a newfound relevance to the field of natural language processing (NLP): recent work suggests some strong-performing recurrent neural networks utilize their memory as counters. Thus, one potential way to…
We present a general framework based on weighted finite automata and weighted finite-state transducers for describing and implementing speech recognizers. The framework allows us to represent uniformly the information sources and data…
We show that a special case of the Feferman-Vaught composition theorem gives rise to a natural notion of automata for finite words over an infinite alphabet, with good closure and decidability properties, as well as several logical…
This paper studies which functions computed by $\mathbb{Z}$-weighted automata can be realized by $\mathbb{N}$-weighted automata, under two extra assumptions: commutativity (the order of letters in the input does not matter) and polynomial…
We establish a general result on the existence of partially defined semiconjugacies between rational functions acting on the Riemann sphere. The semiconjugacies are defined on the complements to at most one-dimensional sets. They are…
A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages.…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
In this paper we study the logical aspects of branching automata, as defined by Lodaya and Weil. We first prove that the class of languages of finite N-free posets recognized by branching automata is closed under complementation. Then we…
Bloch theorem for a periodic operator is being revisited here, and we notice extra orthogonality relationships. It is shown that solutions are bi-periodic, in the sense that eigenfunctions are periodic with respect to one argument, and…
This study evaluates the performance of Recurrent Neural Network (RNN) and Transformer models in replicating cross-language structural priming, a key indicator of abstract grammatical representations in human language processing. Focusing…
The notion of Wheeler languages is rooted in the Burrows-Wheeler transform (BWT), one of the most central concepts in data compression and indexing. The BWT has been generalized to finite automata, the so-called Wheeler automata, by Gagie…
The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics---languages over an…