Lecture 6: Branching Time and CTL

28 January 2010

Update: Revised reference to Fages and Rizk time series paper — see below.

The slides for this lecture review Linear Temporal Logic (LTL), with several examples of LTL formulae for expressing properties of Petri Net behaviour.

Boardwork then gave the expansion from linear time to branching time, the syntax for CTL formulae, and some small discussion of their interpretation.

The final slide gives some further reading, reproduced below. All articles are linked to web pages where you should be able to download copies: you may be asked to log in with the EASE authentication service along the way.

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Lecture 5: Linear Temporal Logic

25 January 2010

The slides for this lecture review the notions of labelled transition systems, runs and traces, and give examples of the expansion of Petri net behaviour into labelled transition systems.

Boardwork then gave definitions of LTL formula, their meaning, and some small examples of application to LTS runs and Petri net behaviours.

Heiner et al. discuss how even finite reachability graphs for Petri nets may blow up very fast (§4(5)). However, they then jump straight to branching-time with CTL.

Huth and Ryan present the syntax and semantics of LTL (§3(2)) as well as some motivation on model checking.

The SPIN tool is based on LTL model checking.

Some Petri Net reading

25 January 2010

Here are some reading indications for the material we have covered so far: Petri Nets, matrix representation, {T,P}-invariants, and the conversion to labelled transition systems.

Lecture notes set 1 and set 2 from a previous iteration of MLCSB cover these topics and include some extra examples.

Chapter 1 introduces and motivates biological modelling in general. Chapter 2 sections 2.1–2.3 describe Petri Nets; the remainder of Chapter 2 discusses representation in the Systems Biology Markup Language (SBML). Wilkinson does not cover logical and model-checking, but does treat probabilistic and stochastic models, which we shall return to later.

Heiner et al.
Sections 1–3 give an overview and some context to modelling in systems biology. Section 4 covers all the Petri Net material we have done so far, and in considerable depth. Read it to see just how detailed these analyses can get.

There are some accompanying slides from this summer school, which you may find helpful.