LPrL: An Asynchronous Linear Time Hyper Logic

Abstract: We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates specify the properties of and the relationships between traces (infinite sequences of actions) using Boolean combinations of LTL formulas. To augment the expressive power of the logic, we introduce a simple language of terms and add the equality predicate t = t' where t and t' are terms. We first illustrate how a number of the security policies as well as a basic consistency property of distributed processes can be captured using LPrL. We then establish our main results using automata theoretic techniques. Namely, the satisfiability and model checking problems for LPrL can be solved in elementary time. These results are in sharp contrast to HyperLTL, the prevalent synchronous hyper linear time logic, whose satisfiability problem is undecidable and whose model checking problem has non-elementary time complexity.