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Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Parsing Expression Grammars (PEGs) are a recognition-based formalism which allows to describe the syntactical and the lexical elements of a language. The main difference between Context-Free Grammars (CFGs) and PEGs relies on the…
Parsing Expression Grammars are a popular foundation for describing syntax. Unfortunately, several syntax of programming languages are still hard to recognize with pure PEGs. Notorious cases appears: typedef-defined names in C/C++,…
Let $S$ be a finite semigroup and let $A$ be a finite dimensional $S$-graded algebra. We investigate the exponential rate of growth of the sequence of graded codimensions $c_n^S(A)$ of $A$, i.e $\lim\limits_{n \rightarrow \infty}…
Instruction sequences with direct and indirect jump instructions are as expressive as instruction sequences with direct jump instructions only. We show that, in the case where the number of instructions is not bounded, we are faced with…
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…
We study sequential programs that are instruction sequences with direct and indirect jump instructions. The intuition is that indirect jump instructions are jump instructions where the position of the instruction to jump to is the content…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
The number of instructions of an instruction sequence is taken for its logical SLOC, and is abbreviated with LLOC. A notion of quantitative expressiveness is based on LLOC and in the special case of operation over a family of single bit…
GP 2 is a non-deterministic programming language for computing by graph transformation. One of the design goals for GP 2 is syntactic and semantic simplicity, to facilitate formal reasoning about programs. In this paper, we demonstrate with…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
Probabilistic circuits (PCs) have emerged as a powerful framework to compactly represent probability distributions for efficient and exact probabilistic inference. It has been shown that PCs with a general directed acyclic graph (DAG)…
The last two decades, since the seminal work of Selig, has seen projective geometric algebra (PGA) gain popularity as a modern coordinate-free framework for doing classical Euclidean geometry and other Cayley-Klein geometries. This…
Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
This paper introduces a computer architecture, where part of the instruction set architecture (ISA) is implemented on small highly-integrated field-programmable gate arrays (FPGAs). Small FPGAs inside a general-purpose processor (CPU) can…
Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…
We introduce Policy Gradient Guidance (PGG), a simple extension of classifier-free guidance from diffusion models to classical policy gradient methods. PGG augments the policy gradient with an unconditional branch and interpolates…
In this work, we give a presentation of the prefix expansion Pr(G) of an inverse semigroup G as recently introduced by Lawson, Margolis and Steinberg which is similar to the universal inverse semigroup defined by the second named author in…