# Supplementary Reading

Here we present pointers to other related reading material, interesting links, etc. Feel free to suggest further additions by writing to us!

### Supplementary Text for the Book

**Additional Remarks on the Linking Combinator**. This short note explains the role played by the relabelling in the definition of the linking combinator used in Exercise 2.13 on page 30 of the book.

**Some Remarks on Time Additivity in Timed Labelled Transition Systems**. This short note discusses some variations on the axioms for timed labelled transition systems, as defined on pages 164-165 of the book.

**SOS Meta-theory: A Very Short Introduction**. This note discusses some possible generalizations of the congruence theorem for bisimilarity over CCS presented in Theorem 3.2, pages 46-49 of the book. It uses this topic to offer a very short introduction to the meta-theory of structural operational semantics.

**Deciding Bisimilarity over Finite Labelled Transition Systems is P-complete**. This note discusses a proof of a result by José L. Balcázar, Joaquim Gabarró and Miklos Santha to the effect that checking various forms of bisimilarity introduced in the book is P-complete.

### Papers in Concurrency Theory

**Computing with actions and communications**by Wan Fokkink and Jan Willem Klop. Proc. Joint BeNeLuxFra Conference on Mathematics, Gent, Bulletin of the Belgian Mathematical Society – Simon Stevin, 13(5):789–805 (December 2006). This paper is an excellent high-level introduction to ACP and its basic theory.

**On the Origins of Bisimulation, Coinduction, and Fixed Points**by Davide Sangiorgi. Technical Report 2007-24, Department of Computer Science, University of Bologna. This paper, which we warmly recommend, is a wonderful exposition on the origins of bisimulation and bisimilarity. It examines the role played by these notions in the three fields where they have been independently discovered: Computer Science, Modal Logic and Set Theory.

**What is this theory good for?**This page offers a collection of links to resources motivating the study of the theory presented in the textbook.

**Papers in the Concurrency Column of the Bulletin of the EATCS**This page offers a collection of links to interesting survey papers that appeared in the Concurrency Column.

**Roadmap of Infinite Results**This is a live survey of known results on the decidability of problems in concurrency theory maintained by Jiri Srba.

**Characteristic Formulae: From Automata to Logic**by Luca Aceto and Anna Ingolfsdottir.

### Papers and Notes on Lattices and Fixed-point Theory

**A lattice-theoretical fixpoint theorem and its applications**by Alfred Tarski. Pacific Journal of Mathematics 5:2: 285–309, 1955. The original reference for the fixed-point theorem presented in Chapter 4 of the book.

**Ordered Sets**by Tero Harju. These are excellent lecture notes covering a substantial amount of material on ordered sets. We recommend them to the mathematically-oriented readers who would like to know more about the mathematics of such structures.

### Books and Lecture Notes

**Communicating Sequential Processes**by C. A. R. Hoare. This book was first published in 1985 by Prentice Hall International and is now freely available on line.