--- res: bibo_abstract: - There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with "controlled-accumulation", allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Udi foaf_name: Boker, Udi foaf_surname: Boker foaf_workInfoHomepage: http://www.librecat.org/personId=31E297B6-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Krishnendu foaf_name: Chatterjee, Krishnendu foaf_surname: Chatterjee foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-4561-241X - 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: Orna foaf_name: Kupferman, Orna foaf_surname: Kupferman bibo_doi: 10.1109/LICS.2011.33 dct_date: 2011^xs_gYear dct_language: eng dct_publisher: IEEE@ dct_title: Temporal specifications with accumulative values@ ...