“…In this setting, weights in weighted transition systems have been most often restricted to range over the nonnegative integers (mostly for representing timing information), and temporal logics have been augmented either with constrained modalities [Koy90,EMSS92] or with explicit variables [AH94], and efficient algorithms have been developed and implemented [BLN03,JLSØ13]. Models with both positive and negative weights have also been studied, but mostly qualitative behaviours alone have been analyzed (this is the case in counter automatasee [HKOW09,GHOW10,Haa12] for recent references), or quantitative constraints have been analyzed (in weighted Kripke structures or games [CDHR10,CRR12]).…”