On the Decidability of Model-Checking Information Flow Properties

Current standard security practices do not provide substantial assurance about information flow security: the end-to-end behavior of a computing system. Noninterference is the basic semantical condition used to account for information flow security. In the literature, there are many definitions of noninterference: Non-inference, Separability and so on. Mantel presented a framework of Basic Security Predicates (BSPs) for characterizing the definitions of noninterference in the literature. Model-checking these BSPs for finite state systems was shown to be decidable in [8]. In this paper, we show that verifying these BSPs for the more expressive system model of pushdown systems is undecidable. We also give an example of a simple security property which is undecidable even for finite-state systems: the property is a weak form of non-inference called WNI, which is not expressible in Mantel’s BSP framework.

A decidable temporal logic with repeating values

Various logical formalisms with the freeze quantifier have been recently considered to model computer systems even though this is a powerful mechanism that often leads to undecidability. In this paper, we study a linear-time temporal logic with past-time operators such that the freeze operator is only used to express that some value from an infinite set is repeated in the future or in the past. Such a restriction has been inspired by a recent work on spatio-temporal logics. We show decidability of finitary and infinitary satisfiability by reduction into the verification of temporal properties in Petri nets. This is a surprising result since the logic is closed under negation, contains future-time and past-time temporal operators and can express the nonce property and its negation. These ingredients are known to lead to undecidability with a more liberal use of the freeze quantifier.

Temporal Logics of Repeating Values

Various logical formalisms with the freeze quantifier have been recently considered to model computer systems even though this is a powerful mechanism that often leads to undecidability. In this article, we study a linear-time temporal logic with past-time operators such that the freeze operator is only used to express that some value from an infinite set is repeated in the future or in the past. Such a restriction has been inspired by a recent work on spatio-temporal logics that suggests such a restricted use of the freeze operator. We show decidability of finitary and infinitary satisfiability by reduction into the verification of temporal properties in Petri nets by proposing a symbolic representation of models. This is a quite surprising result in view of the expressive power of the logic since the logic is closed under negation, contains future-time and past-time temporal operators and can express the nonce property and its negation. These ingredients are known to lead to undecidability with a more liberal use of the freeze quantifier. The article also contains developments about the relationships between temporal logics with the freeze operator and counter automata as well as reductions into first-order logics over data words.