Related papers: Regular Combinators for String Transformations
Nested relations, built up from atomic types via product and set types, form a rich data model. Over the last decades the nested relational calculus, NRC, has emerged as a standard language for defining transformations on nested…
We combine the language of monoids with the language of preorders so as to refine some fundamental aspects of the classical theory of factorization and prove an abstract factorization theorem with a variety of applications. In particular,…
In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…
In the well-known construction of the field of fractions of an integral domain, division by zero is excluded. We introduce "fracpairs" as pairs subject to laws consistent with the use of the pair as a fraction, but do not exclude…
A "blendstring" is a piecewise polynomial interpolant with high-degree two-point Hermite interpolational polynomials on each piece, analogous to a cubic spline. Blendstrings are smoother and can be more accurate than cubic splines, and can…
Transducers extend finite state automata with outputs, and describe transformations from strings to strings. Sequential transducers, which have a deterministic behaviour regarding their input, are of particular interest. However, unlike…
Call a noncommutative rational function $r$ regular if it has no singularities, i.e., $r(X)$ is defined for all tuples of self-adjoint matrices $X$. In this article regular noncommutative rational functions $r$ are characterized via the…
Clones of functions play a foundational role in both universal algebra and theoretical computer science. In this work, we introduce clone merge monoids (cm-monoids), a unifying one-sorted algebraic framework that integrates abstract clones,…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
Agda's standard library struggles in various places with n-ary functions and relations. It introduces congruence and substitution operators for functions of arities one and two, and provides users with convenient combinators for…
We study deformations of closed string theory by primary fields of conformal weight $(1,1)$, using conformal techniques on the complex plane. A canonical surface integral formalism for computing commutators in a non-holomorphic theory is…
Modular operads relevant to string theory can be equipped with an additional structure, coming from the connected sum of surfaces. Motivated by this example, we introduce a notion of connected sum for general modular operads. We show that a…
We study the fundamental issue of decidability of satisfiability over string logics with concatenations and finite-state transducers as atomic operations. Although restricting to one type of operations yields decidability, little is known…
We give a domain-theoretic semantics to a statistical programming language, using the plain old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably, our monad of minimal valuations is commutative, which…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
The summatory function of a $q$-regular sequence in the sense of Allouche and Shallit is analysed asymptotically. The result is a sum of periodic fluctuations for eigenvalues of absolute value larger than the joint spectral radius of the…
These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…
Deterministic two-way transducers with pebbles (aka pebble transducers) capture the class of polyregular functions, which extend the string-to-string regular functions allowing polynomial growth instead of linear growth. One of the most…
To apply neural sequence models such as the Transformers to music generation tasks, one has to represent a piece of music by a sequence of tokens drawn from a finite set of pre-defined vocabulary. Such a vocabulary usually involves tokens…
The regular spanners (characterised by vset-automata) are closed under the algebraic operations of union, join and projection, and have desirable algorithmic properties. The core spanners (introduced by Fagin, Kimelfeld, Reiss, and…