Related papers: Regular and First Order List Functions
First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…
This paper is about certain string-to-string functions, called the polyregular functions. These are like the regular string-to-string functions, except that they can have polynomial (and not just linear) growth. The class has four…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
Regular functions of infinite words are (partial) functions realized by deterministic two-way transducers with infinite look-ahead. Equivalently, Alur et. al. have shown that they correspond to functions realized by deterministic Muller…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…
A word-to-word function is rational if it can be realized by a non-deterministic one-way transducer. Over finite words, it is a classical result that any rational function is regular, i.e. it can be computed by a deterministic two-way…
We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
Compared to functions in mathematics, functions in programming languages seem to be under classified. Functional programming languages based on the lambda calculus famously treat functions as first-class values. Object-oriented languages…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
We focus on (partial) functions that map input strings to a monoid such as the set of integers with addition and the set of output strings with concatenation. The notion of regularity for such functions has been defined using two-way…
We give a new characterization of the class of rational string functions from formal language theory using order-preserving interpretations with respect to a very weak monadic programming language. This refines the known characterization of…
What should a function that extrapolates beyond known input/output examples look like? This is a tricky question to answer in general, as any function matching the outputs on those examples can in principle be a correct extrapolant. We…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
We present a size-aware type system for first-order shapely function definitions. Here, a function definition is called shapely when the size of the result is determined exactly by a polynomial in the sizes of the arguments. Examples of…
We describe Query Defunctionalization which enables off-the-shelf first-order database engines to process queries over first-class functions. Support for first-class functions is characterized by the ability to treat functions like regular…
Functional transductions realized by two-way transducers (or, equally, by streaming transducers or MSO transductions) are the natural and standard notion of "regular" mappings from words to words. It was shown in 2013 that it is decidable…
A rational function is the ratio of two complex polynomials in one variable without common roots. Its degree is the maximum of the degrees of the numerator and the denominator. Rational functions belong to the same class if one turns into…
We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…