Abstract
Trace expressions are a compact and expressive formalism, initially devised for runtime verification of agent interactions in multiagent systems, which has been successfully employed to model real protocols, and to generate monitors for mainstream multiagent system platforms, and generalized to support runtime verification of different kinds of properties and systems.
In this paper we formally compare the expressive power of trace expressions with the Linear Temporal Logic (LTL), a formalism widely adopted in runtime verification. We show that any LTL formula can be translated into a trace expression which is equivalent from the point of view of runtime verification. Since trace expressions are able to express and verify sets of traces that are not context-free, we can derive that in the context of runtime verification trace expressions are more expressive than LTL.
Partly funded by “Progetto MIUR PRIN CINA Prot. 2010LHT4KM”.
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Notes
- 1.
Here, for simplicity, an event does not include the signature of the method as it should be the case for those languages supporting static overloading.
- 2.
Binary operators associate from left, and are listed in decreasing order of precedence, that is, the first operator has the highest precedence.
- 3.
For efficiency reasons, our implementation exploits simplification opportunities after each transition step, therefore in practice for this example the two transitions would lead to the same expression.
- 4.
Recall that for a comparison with context-free languages we need to disregard infinite traces; for instance, \( a\_or\_b {\gg } AB \) and \( b\_or\_c {\gg } BC \) contain also the infinite traces \(a^\omega \) and \(b^\omega \), respectively.
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Ancona, D., Ferrando, A., Mascardi, V. (2016). Comparing Trace Expressions and Linear Temporal Logic for Runtime Verification. In: Ábrahám, E., Bonsangue, M., Johnsen, E. (eds) Theory and Practice of Formal Methods. Lecture Notes in Computer Science(), vol 9660. Springer, Cham. https://doi.org/10.1007/978-3-319-30734-3_6
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