Related papers: Numeration systems on a regular language
Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…
We describe a method for solving linear systems over the localization of a commutative ring $R$ at a multiplicatively closed subset $S$ that works under the following hypotheses: the ring $R$ is coherent, i.e., we can compute finite…
This work attempts to explain the types of computation that neural networks can perform by relating them to automata. We first define what it means for a real-time network with bounded precision to accept a language. A measure of network…
We introduce formal languages over infinite alphabets where words may contain binders. We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata)…
It is known that an ordinal is the order type of the lexicographic ordering of a regular language if and only if it is less than omega^omega. We design a polynomial time algorithm that constructs, for each well-ordered regular language L…
For a system to understand natural language, it needs to be able to take natural language text and answer questions given in natural language with respect to that text; it also needs to be able to follow instructions given in natural…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
In this note, we present a characterization of sets definable in Skolem arithmetic, i.e., the first-order theory of natural numbers with multiplication. This characterization allows us to prove the decidability of the theory. The idea is…
In this paper we consider the class of lambda-nondeterministic linear automata as a model of the class of linear languages. As usual in other automata models, lambda-moves do not increase the acceptance power. The main contribution of this…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
Can recurrent neural nets, inspired by human sequential data processing, learn to understand language? We construct simplified datasets reflecting core properties of natural language as modeled in formal syntax and semantics: recursive…
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
Complex structures are typical in machine learning. Tailoring learning algorithms for every structure requires an effort that may be saved by defining a generic learning procedure adaptive to any complex structure. In this paper, we propose…
Contrary to popular misconception, the question in the title is far from simple. It involves sets of numbers on the first level, sets of sets of numbers on the second level, and so on, endlessly. The infinite hierarchy of the levels…
It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized…
We present algorithms for efficiently learning regularizers that improve generalization. Our approach is based on the insight that regularizers can be viewed as upper bounds on the generalization gap, and that reducing the slack in the…
We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characterized in terms of its formal power series solutions. We also…
This paper considers finite-automata based algorithms for handling linear arithmetic with both real and integer variables. Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this…
I propose a class of non-positional numeral systems where numbers are represented by Dyck words, with the systems arising from a recursive extension of prime factorization. After describing two proper subsets of the Dyck language capable of…
Regular sequences generalize the extensively studied automatic sequences. Let $S$ be an abstract numeration system. When the numeration language $L$ is prefix-closed and regular, a sequence is said to be $S$-regular if the module generated…