Abstract
Temporal logic has become a well-established method for specifying the behavior of distributed systems. In this paper, we interpret a temporal logic over a partial order model that is a trace system. The satisfaction of the formulae is directly defined on traces on the basis of rewriting rules; so, the graph representation of the system can be completely avoided; moreover, a method is presented that keeps the trace system finite, also in the presence of infinite computations. To further reduce the complexity of model checking temporal logic formulae, an abstraction technique is applied to trace systems.
Highlights
Introduction and MotivationLinear time [1] and branching time [2] temporal logics are used for specifying and verifying concurrent and distributed systems: partial order models are mostly used to give semantics to linear time logics, while interleaving models are widely used for branching time logics
Model checking is one of the main methods for the automated verification of concurrent systems [5]; it consists in checking whether a structure representing the system is a model for a logic formula
A variety of methods for reducing the state explosion problem have been developed [6,7,8,9,10]; in the context of branching time logics, in [11,12], the authors and others proposed a logic, called selective mu-calculus, equi-expressive to mu-calculus [13], but, such that each formula directly characterizes an abstraction of the system that maintains the truth value of the formula itself
Summary
Linear time [1] and branching time [2] temporal logics are used for specifying and verifying concurrent and distributed systems: partial order models (trace systems are an example) are mostly used to give semantics to linear time logics, while interleaving models (such as transition systems) are widely used for branching time logics. A variety of methods for reducing the state explosion problem have been developed [6,7,8,9,10]; in the context of branching time logics, in [11,12], the authors and others proposed a logic, called selective mu-calculus, equi-expressive to mu-calculus [13], but, such that each formula directly characterizes an abstraction of the system that maintains the truth value of the formula itself. We give a non-interleaving interpretation of selective mu-calculus formulae using the simplest and best known partial order model for computations, that is Mazurkiewicz’s trace system [3,15,20] This model allows a compact representation of the system computations using only an element, called trace, to represent an equivalence class of sequences of events with respect to a dependence relation. The last section contains conclusions and comparisons of the presented approach with some related works
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
