Abstract
Formal verification methods have often focused on qualitative properties such as constraints on the order of event occurrences. On the other hand, it is also required in practice to verify quantitative properties on performances of systems, to analyze the performances quantitatively, or to optimize them. In this article, we develop LTLmp that is an LTL extension with mean-payoff formulae for describing quantitative properties on long-run average cost and frequency of event occurrences. In addition, we develop effective algorithms to solve LTLmp model-checking, satisfiability-checking and optimization problems.
