DeepAI
Log In Sign Up

A String Diagrammatic Axiomatisation of Finite-State Automata

09/30/2020
by   Robin Piedeleu, et al.
0

We develop a fully diagrammatic approach to the theory of finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. Moreover, we provide an equational theory that completely axiomatises language equivalence in this new setting. This theory has two notable features. First, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks. Second, the proposed axiomatisation is finitary – a result which is provably impossible to obtain for the one-dimensional syntax of regular expressions.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/04/2019

Bialgebraic Semantics for String Diagrams

Turi and Plotkin's bialgebraic semantics is an abstract approach to spec...
09/02/2015

Confluent Orthogonal Drawings of Syntax Diagrams

We provide a pipeline for generating syntax diagrams (also called railro...
11/08/2021

Solving String Constraints With Regex-Dependent Functions Through Transducers With Priorities And Variables

Regular expressions are a classical concept in formal language theory. R...
01/29/2020

Extended Algebraic State Transition Diagrams

Algebraic State-Transition Diagrams (ASTDs) are extensions of common aut...
06/04/2020

Twinning automata and regular expressions for string static analysis

In this paper we formalize and prove the soundness of Tarsis, a new abst...
10/26/2020

A Purely Regular Approach to Non-Regular Core Spanners

The regular spanners (characterised by vset-automata) are closed under t...