Handbook of Truly Concurrent Process Algebra

Chapter 2: Backgrounds

Abstract

This chapter introduces the preliminaries of algebraic theory for reversible computing.

Keywords

Reversible Computing; Algebraic Theory; Axiomatization

In this chapter, we introduce some preliminaries for self-sufficiency.

2.1 Operational semantics

Definition 2.1

Congruence

Let Σ be a signature. An equivalence relation R on $\mathcal{T}(\mathrm{\Sigma })$ is a congruence if for each $f\in \mathrm{\Sigma }$, if $s_{i}R{t}_i$ for $i\in \{1,\cdots ,ar(f)\}$, then $f(s_1,\cdots ,s_{ar(f)})Rf(t_1,\cdots ,t_{ar(f)})$