Finite trace observations induce the Cantor topology on infinite traces while simulation observations generate a finer topology, with a general theorem equating open sets to finitely verifiable properties.
The complexity of being monitorable
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abstract
We study monitorable sets from a topological standpoint. In particular, we use descriptive set theory to describe the complexity of the family of monitorable sets in a countable space $X$. When $X$ is second countable, we observe that the family of monitorable sets is $\Pi^0_3$ and determine the exact complexities it can have. In contrast, we show that if $X$ is not second countable then the family of monitorable sets can be much more complex, giving an example where it is $ \Pi^1_1$-complete.
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cs.LO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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A Topological Framework for Finite Behavioural Observations and Verification
Finite trace observations induce the Cantor topology on infinite traces while simulation observations generate a finer topology, with a general theorem equating open sets to finitely verifiable properties.