Applications of the Differential Calculus in the Study of the Timed Automata: the Inertial Delay Buffer

TL;DR

This paper explores the application of differential calculus to characterize the simplest timed automaton, the inertial delay buffer, using derivatives of R->{0,1} functions in both deterministic and non-deterministic forms.

Contribution

It introduces a novel approach to analyze timed automata through derivatives of R->{0,1} functions, providing a new mathematical framework.

Findings

Characterization of inertial delay buffer automaton

Derivation of relations using derivatives of R->{0,1} functions

Comparison between deterministic and non-deterministic models

Abstract

We write the relations that characterize the simpliest timed automaton, the inertial delay buffer, in two versions: the non-deterministic and the deterministic one, by making use of the derivatives of the R->{0,1} functions.