Model composition in model checking
Year: 2014
Type: dissertation
Abstract: Model-checking allows one to formally check properties of systems: these properties are modeled as logic formulas and the systems as structures like transition systems. These transition systems are often composed, i.e., they arise in form of products or sums. The composition technique allows us to deduce the truth of a formula in the composed system from "interface information": the truth of formulas for the component systems and information in which components which of these formulas hold. We are interested in identifying situations where the composition technique works in the context of model-checking (reachability properties, linear and branching time temporal logic) and, in these cases, how large the interface information can become. In the first main part of this thesis, we extend known results for synchronized products of transition systems by showing a composition theorem for finitely synchronized products and first-order logic (or modal logic) extended by regular reachability over a unary alphabet. We further show that the composition technique fails for two generalizations of the logic: in the general case of regular reachability and in the case of propositional dynamic logic over a unary alphabet. Furthermore, it fails for synchronized products which are not finitely synchronized. A known drawback of the composition technique is the growth of the size of the generated interface information in relation to the given formula. Göller, Jung and Lohrey have shown a non-elementary lower bound for this size in general for first-order logic (for products) and modal logic (for disjoint ordered sums). In the second and third part of this thesis, we look at combinations of logics and systems where we can avoid this. In the second part, we show a composition theorem for linear temporal logic (LTL) and disjoint ordered sums of words. A careful analysis shows that, here, the size of the interface information only grows at most exponential in the size of the given formula. In the third part, we generalize this composition technique to a disjoint ordered sum of trees and computation tree logic (CTL). Here, we deal with trees as components which are composed via a tree structure. We show a composition result for which the interface information grows exponentially in the size of the given formula and in the branching of the index tree structure.
Source: RWTH Publications (RWTH Aachen)
Authors: Ingo Felscher, Wolfgang Thomas
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W324774994