10 research outputs found
Fixpoint Alternation: Arithmetic, Transition Systems, and the Binary Tree
We provide an elementary proof of the fixpoint alternationhierarchy in arithmetic, which in turn allows us to simplify the proof of the modal mu-calculus alternation hierarchy. We further show that the alternation hierarchy on the binary tree is strict, resolving a problem of Niwinski
Automated Synthesis of Enforcing Mechanisms for Security Properties in a Timed Setting
AbstractIn [Martinelli, F. and I. Matteucci, Modeling security automata with process algebras and related results (2006), presented at the 6th International Workshop on Issues in the Theory of Security (WITS '06) - Informal proceedings; Martinelli, F. and I. Matteucci, Through modeling to synthesis of security automata (2006), accepted to STM06. To appeare in ENTCS] we have presented an approach for enforcing security properties. It is based on the automatic synthesis of controller programs that are able to detect and eventually prevent possible wrong action performed by an external agent. Here, we extend this approach also to a timed setting. Under certain assumptions, we are also able to enforce several information flow properties. We show how to deal with parameterized systems
The modal mu-calculus alternation hierarchy is strict
AbstractOne of the open questions about the modal mu-calculus is whether the alternation hierarchy collapses; that is, whether all modal fixpoint properties can be expressed with only a few alternations of least and greatest fixpoints. In this paper, we resolve this question by showing that the hierarchy does not collapse
Exptime tableaux for the coalgebraic μ-calculus
The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this paper, we introduc
Finite-State Abstractions for Probabilistic Computation Tree Logic
Probabilistic Computation Tree Logic (PCTL) is the established temporal
logic for probabilistic verification of discrete-time Markov chains. Probabilistic
model checking is a technique that verifies or refutes whether a property
specified in this logic holds in a Markov chain. But Markov chains are often
infinite or too large for this technique to apply. A standard solution to
this problem is to convert the Markov chain to an abstract model and to
model check that abstract model. The problem this thesis therefore studies
is whether or when such finite abstractions of Markov chains for model
checking PCTL exist.
This thesis makes the following contributions. We identify a sizeable fragment
of PCTL for which 3-valued Markov chains can serve as finite abstractions;
this fragment is maximal for those abstractions and subsumes many
practically relevant specifications including, e.g., reachability. We also develop
game-theoretic foundations for the semantics of PCTL over Markov
chains by capturing the standard PCTL semantics via a two-player games.
These games, finally, inspire a notion of p-automata, which accept entire
Markov chains. We show that p-automata subsume PCTL and Markov
chains; that their languages of Markov chains have pleasant closure properties;
and that the complexity of deciding acceptance matches that of probabilistic
model checking for p-automata representing PCTL formulae. In addition,
we offer a simulation between p-automata that under-approximates
language containment. These results then allow us to show that p-automata
comprise a solution to the problem studied in this thesis
Modal Action Logics for Reasoning about Reactive Systems
Meyer, J-.J.Ch. [Promotor]Riet, R.P. [Promotor]van de Wieringa, R. [Promotor
On the expressivity of the modal mu-calculus
SIGLEAvailable from British Library Document Supply Centre-DSC:5186.0913(EU-ECS-LFCS--95-338) / BLDSC - British Library Document Supply CentreGBUnited Kingdo