Related papers: Deterministic regular functions of infinite words

Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…

Martin's Conjecture states that every definable function on the Turing degrees is either constant or increasing, and that every increasing function is an iterate of the Turing jump. This classification has already been corroborated for the…

Skolem functions play a central role in the study of first order logic, both from theoretical and practical perspectives. While every Skolemized formula in first-order logic makes use of Skolem constants and/or functions, not all such…

We study rational functions admitting a continuous extension to the real affine space. First of all, we focus on the regularity of such functions exhibiting some nice properties of their partial derivatives. Afterwards, since these…

A new pair of asymptotic invariants for finitely presented groups, called intrinsic and extrinsic tame filling functions, are introduced. These filling functions are quasi-isometry invariants that strengthen the notions of intrinsic and…

We define representations of continuous functions on infinite streams of discrete values, both in the case of discrete-valued functions, and in the case of stream-valued functions. We define also an operation on the representations of two…

Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a…

We say that a set is exhaustible if it admits algorithmic universal quantification for continuous predicates in finite time, and searchable if there is an algorithm that, given any continuous predicate, either selects an element for which…

The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…

Multidimensional continuous-domain inverse problems are often solved by the minimization of a loss functional, formed as the sum of a data fidelity and a regularization. In this work, we present a new construction where the regularization…

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…

Altenbernd, Thomas and W\"ohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with usual acceptance conditions, such as the B\"uchi and Muller ones [1]. It was proved…

Regular expressions are a classical concept in formal language theory. Regular expressions in programming languages (RegEx) such as JavaScript, feature non-standard semantics of operators (e.g. greedy/lazy Kleene star), as well as…

We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. We focus on the case where the escape is degenerate in the sense that points from…

We prove a characterization of first-order string-to-string transduction via $\lambda$-terms typed in non-commutative affine logic that compute with Church encoding, extending the analogous known characterization of star-free languages. We…

Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…

Deterministic and nondeterministic finite automata with translucent letters were introduced by Nagy and Otto more than a decade ago as Cooperative Distributed systems of a kind of stateless restarting automata with window size one. These…

This paper studies the problem of learning computable functions in the limit by extending Gold's inductive inference framework to incorporate \textit{computational observations} and \textit{restricted input sources}. Complimentary to the…

Motivated by the successful application of the theory of regular languages to formal verification of finite-state systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can…

Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing basic arithmetic. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities,…