--- res: bibo_abstract: - 'Quantitative monitoring can be universal and approximate: For every finite sequence of observations, the specification provides a value and the monitor outputs a best-effort approximation of it. The quality of the approximation may depend on the resources that are available to the monitor. By taking to the limit the sequences of specification values and monitor outputs, we obtain precision-resource trade-offs also for limit monitoring. This paper provides a formal framework for studying such trade-offs using an abstract interpretation for monitors: For each natural number n, the aggregate semantics of a monitor at time n is an equivalence relation over all sequences of at most n observations so that two equivalent sequences are indistinguishable to the monitor and thus mapped to the same output. This abstract interpretation of quantitative monitors allows us to measure the number of equivalence classes (or “resource use”) that is necessary for a certain precision up to a certain time, or at any time. Our framework offers several insights. For example, we identify a family of specifications for which any resource-optimal exact limit monitor is independent of any error permitted over finite traces. Moreover, we present a specification for which any resource-optimal approximate limit monitor does not minimize its resource use at any time. @eng' bibo_authorlist: - foaf_Person: foaf_givenName: Thomas A foaf_name: Henzinger, Thomas A foaf_surname: Henzinger foaf_workInfoHomepage: http://www.librecat.org/personId=40876CD8-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-2985-7724 - foaf_Person: foaf_givenName: Nicolas Adrien foaf_name: Mazzocchi, Nicolas Adrien foaf_surname: Mazzocchi foaf_workInfoHomepage: http://www.librecat.org/personId=b26baa86-3308-11ec-87b0-8990f34baa85 - foaf_Person: foaf_givenName: Naci E foaf_name: Sarac, Naci E foaf_surname: Sarac foaf_workInfoHomepage: http://www.librecat.org/personId=8C6B42F8-C8E6-11E9-A03A-F2DCE5697425 bibo_doi: 10.1007/978-3-031-17196-3_11 bibo_volume: 13498 dct_date: 2022^xs_gYear dct_identifier: - UT:000866539700011 dct_isPartOf: - http://id.crossref.org/issn/0302-9743 dct_language: eng dct_publisher: Springer Nature@ dct_title: Abstract monitors for quantitative specifications@ ...