Related papers: Monadic Expressions and their Derivatives

We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…

Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…

A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…

We extend Antimirov's partial derivatives from regular expressions to $\mu$-regular expressions that describe context-free languages. We prove the correctness of partial derivatives as well as the finiteness of the set of iterated partial…

Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…

Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…

Automatic differentiation (AD) has been a topic of interest for researchers in many disciplines, with increased popularity since its application to machine learning and neural networks. Although many researchers appreciate and know how to…

We introduce constructive and classical systems for nonstandard arithmetic and show how variants of the functional interpretations due to Goedel and Shoenfield can be used to rewrite proofs performed in these systems into standard ones.…

This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…

The aim of the paper is to build a connection between two approaches towards categorical language theory: the coalgebraic and algebraic language theory for monads. For a pair of monads modelling the branching and the linear type we defined…

We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…

Monads are extensively used nowadays to abstractly model a wide range of computational effects such as nondeterminism, statefulness, and exceptions. It turns out that equipping a monad with a (uniform) iteration operator satisfying a set of…

Probabilistic programming and the formal analysis of probabilistic algorithms are active areas of research, driven by the widespread use of randomness to improve performance. While functional correctness has seen substantial progress,…

Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…

We introduce a new technique for constructing a finite state deterministic automaton from a regular expression, based on the idea of marking a suitable set of positions inside the expression, intuitively representing the possible points…

We study the operad of associative algebras equipped with a derivation. We show that it is determined by polynomials in several variables and substitution. Replacing polynomials by rational functions gives an operad which is isomorphic to…

This report is mostly written for educational purposes. It is meant as a self contained introduction to regular languages, regular expressions, and regular expression matching by using Brzozowski derivatives. As such it is mostly based on…

Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…

The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation…

Multi-tildes are regular operators that were introduced to enhance the factorization power of regular expressions, allowing us to add the empty word in several factors of a catenation product of languages. In addition to multi-bars, which…