Quantitative verification

Abstract

Automated verification is a technique for establishing if certain properties, usually expressed in temporal logic, hold for a system model. The model can be defined using a high-level formalism or extracted directly from software using methods such as abstract interpretation. The verification proceeds through exhaustive exploration of the state-transition graph of the model and is therefore more powerful than testing. Quantitative verification is an analogous technique for establishing quantitative properties of a system model, such as the probability of battery power dropping below minimum, the expected time for message delivery and the expected number of messages lost before protocol termination. Models analysed through this method are typically variants of Markov chains, annotated with costs and rewards that describe resources and their usage during execution. Properties are expressed in temporal logic extended with probabilistic and reward operators. Quantitative verification involves a combination of a traversal of the state-transition graph of the model and numerical computation. This paper gives a brief overview of current research in quantitative verification, concentrating on the potential of the method and outlining future challenges. The modelling approach is described and the usefulness of the methodology illustrated with an example of a real-world protocol standard -Bluetooth device discovery -that has been analysed using the PRISM model checker (www.prismmodelchecker.org).

Behavioural Computer Science: an agenda for combining modelling of human and system behaviours

“…• One alternative is to use weights and weighted models [69,70]. We would then need empirical methods for automatically learning the weights as well as for measuring the importance/weight of the respective aspect.…”

Formalizing and Reasoning about Quality

“…In fuzzy temporal logic [22], the atomic propositions take values in [0,1]. Probabilistic temporal logic is interpreted over Markov decision processes [8,20], and in the context of real-valued signals [11], quantitativeness stems from both time intervals and predicates over the value of atomic propositions.…”