Related papers: Numeration-automatic sequences
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
We introduce the class of P-finite automata. These are a generalisation of weighted automata, in which the weights of transitions can depend polynomially on the length of the input word. P-finite automata can also be viewed as simple…
We extend the L* algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids…
Two new classes of finite automata, called General hexagonal Boustrophedon finite automata and General hexagonal returning finite automata operating on hexagonal grids, are introduced and analyzed. The work establishes the theoretical…
When humans perform inductive learning, they often enhance the process with background knowledge. With the increasing availability of well-formed collaborative knowledge bases, the performance of learning algorithms could be significantly…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
In a jumping finite automaton, the input head can jump to an arbitrary position within the remaining input after reading and consuming a symbol. We characterize the corresponding class of languages in terms of special shuffle expressions…
Language models and conversational systems are growing increasingly advanced, creating outputs that may be mistaken for humans. Consumers may thus be misled by advertising, media reports, or vagueness regarding the role of automation in the…
We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.
We introduce and study the essential inputs (variables) for terms (trees) and tree automata.
We introduce a method for using deep neural networks to amortize the cost of inference in models from the family induced by universal probabilistic programming languages, establishing a framework that combines the strengths of probabilistic…
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…
A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In previous work, we proved the pendant of this theorem in a setting with interaction:…
Computer science class enrollments have rapidly risen in the past decade. With current class sizes, standard approaches to grading and providing personalized feedback are no longer possible and new techniques become both feasible and…
We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal interpretations and some research directions.…
A two-dimensional arrangement of toothpicks is constructed by the following iterative procedure. At stage 1, place a single toothpick of length 1 on a square grid, aligned with the y-axis. At each subsequent stage, for every exposed…
Neural sequence-to-sequence systems deliver state-of-the-art performance for automatic speech recognition. When using appropriate modeling units, e.g., byte-pair encoding, these systems are in principle open vocabulary systems. In practice,…
The major system is a mnemonic system that can be used to memorize sequences of numbers. In this work, we present a method to automatically generate sentences that encode a given number. We propose several encoding models and compare the…
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating…
The transition structure of an automaton can be used to create a natural topology to the set of states of an automaton, generating, this way, a topological space. Probabilistic automata can also be modeled in terms of measure theory. A…