Computation tree measurement language (CTML)

• Published in: Formal aspects of computing Vol. 30; no. 3-4; pp. 443 - 462
• Main Authors: Jing, Yaping, Miner, Andrew S.
• Format: Journal Article
• Language: English
• Published: London Springer London 01.08.2018; Association for Computing Machinery
• Subjects: Computer Science; Logic programming; Math Applications in Computer Science; Operators (mathematics); Original Article; Performance evaluation; Probabilistic models; Probability theory; Queries; Set theory; Specification and description languages; Theory of Computation; Probabilistic model checking; Markov chains; Performance measures
• ISSN: 0934-5043; 1433-299X
• DOI: 10.1007/s00165-018-0457-3

In this work, we present a formal language, CTML, to reason over probabilistic systems. CTML extends stochastic temporal logics in a way that it takes a real value as input and output a real value in the range of [ 0 , ∞ ) , as opposed to 0/1 values as input and output, and it can nest real values. This allows CTML to express a rich set of queries towards the unification of model checking and performance evaluation. In fact, CTML covers PCTL. It can express a nontrivial subset of PLTL formulas that cannot be expressed by PCTL. The significance of this result is that the overall complexity of CTML is linear, as opposed to exponential as it is with PLTL, in the size of the operators for a given formula, and polynomial in the size of a given model. Moreover, CTML can express real-valued performance queries such as: “if a system encounters a failure, what is the expected time to reach a recovery state?” that cannot be expressed by a probabilistic model checking logic, because they are “probabilistic” at most. Along with the specification language, we present a set of algorithms for the evaluation of the language and show proofs for their correctness. Additionally, we include an application example and show experimental results.