Flatness Is Not a Weakness

We propose an extension, called L + p , of the temporal logic LTL, which enables talking about nitely many register values: the models are innnite words over tuples of integers (resp. real numbers). The formulas of L + p are at: on the left of an until, only atomic formulas or LTL formulas are allowed. We prove, in the spirit of the correspondence between automata and temporal logics, that the models of a L + p formula are recognized by a piecewise at counter machine; for each state q, at most one loop of the machine on q may modify the register values. Emptiness of (piecewise) at counter machines is decidable (this follows from a result in 9]). It follows that satissability and model-checking the negation of a formula are decidable for L + p. On the other hand, we show that inclusion is undecidable for such languages. This shows that validity and model-checking positive formulas are undecidable. logic in computer science.