DeepAI
Log In Sign Up

The Complexity of Monitoring Hyperproperties

01/19/2021
by   Borzoo Bonakdarpour, et al.
0

We study the runtime verification of hyperproperties, expressed in the temporal logic HyperLTL, as a means to inspect a system with respect to security polices. Runtime monitors for hyperproperties analyze trace logs that are organized by common prefixes in the form of a tree-shaped Kripke structure, or are organized both by common prefixes and by common suffixes in the form of an acyclic Kripke structure. Unlike runtime verification techniques for trace properties, where the monitor tracks the state of the specification but usually does not need to store traces, a monitor for hyperproperties repeatedly model checks the growing Kripke structure. This calls for a rigorous complexity analysis of the model checking problem over tree-shaped and acyclic Kripke structures. We show that for trees, the complexity in the size of the Kripke structure is L-complete independently of the number of quantifier alternations in the HyperLTL formula. For acyclic Kripke structures, the complexity is PSPACE-complete (in the level of the polynomial hierarchy that corresponds to the number of quantifier alternations). The combined complexity in the size of the Kripke structure and the length of the HyperLTL formula is PSPACE-complete for both trees and acyclic Kripke structures, and is as low as NC for the relevant case of trees and alternation-free HyperLTL formulas. Thus, the size and shape of both the Kripke structure and the formula have significant impact on the complexity of the model checking problem.

READ FULL TEXT
12/14/2010

On the size of data structures used in symbolic model checking

Temporal Logic Model Checking is a verification method in which we descr...
05/30/2018

Approximate LTL model checking

Linear Temporal Logic (LTL) model checking has been applied to many fiel...
09/20/2021

A Parameterized View on the Complexity of Dependence Logic

In this paper, we investigate the parameterized complexity of model chec...
07/13/2017

Parsing with Traces: An O(n^4) Algorithm and a Structural Representation

General treebank analyses are graph structured, but parsers are typicall...
01/30/2019

A Constructive Equivalence between Computation Tree Logic and Failure Trace Testing

The two major systems of formal verification are model checking and alge...
01/19/2021

Program Repair for Hyperproperties

We study the repair problem for hyperproperties specified in the tempora...
02/16/2017

Courcelle's Theorem Made Dynamic

Dynamic complexity is concerned with updating the output of a problem wh...