Lecture 11: Markov Chains and Stochastic Logics

18 February 2010

Small Petri net example in the form of a signal cascade. Extracting from this in turn: a transition system; a DTMC with transition probabilities; and a CTMC with rates. Corresponding refinements of temporal logic: LTL/CTL; PCTL with probabilities; CSL with probabilities and duration. How this extends expressiveness, and how replacing discrete “always” with probabilistic “almost surely” gives results more closely matching intuition.

Probabilistic symbolic model checking and the PRISM tool. Examples from:


Read the remainder of the Kwiatkowska et al. tutorial, §§4–6.

Also, recall this short report:

In the meantime, however, Fisher and her fellow executable-biology enthusiasts have a lot of convincing to do, says Stephen Oliver, a biologist at the University of Cambridge, UK. “Modelling in general is regarded sceptically by many biologists,” he points out.

Do you think this is true? Can you find any evidence for or against?

Lecture 8: Mix, match and use temporal logics

6 February 2010

Revisit example valuation of CTL formula, now corrected. Further possible logics: Hennessy-Milner, modal μ-calculus, and monadic second-order logic. Presentation of syntax, semantics, and small examples. Relative expressiveness. Mixing and matching modalities and operators for convenience, distinct from expressiveness: CTL- as an example.

Application to specific biological models, as discussed in these articles: Fages and Rizk evaluating LTL formulae over time series data; de Jong et al. on mapping textual descriptions into CTL.

Link: Slides

Lecture 7: From LTL and CTL to CTL*

2 February 2010

Review and comparison of the syntax and semantics of temporal logics LTL and CTL. Distinction between the direct observability of individual runs, and the assessment of alternative possibilities in branching-time logics like CTL. Valuation of CTL formulae on specific transition systems. Distinct expressiveness of LTL and CTL: example to show AF AG is not AFG.

Link: Slides (with CTL valuation table corrected)


Two items to read for Thursday:

The first of these is an invited conference talk, giving an overview of some work on applying model-checking to problems in systems biology. The second is a more detailed article on the material.

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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