Study on the Safety Problem of Access Matrix Models

访问矩阵模型中的安全问题是确定给定主体最终是否能够获得对给定对象的访问权限。总的来说，不幸的是，安全问题是无法确定的。除了强约束系统（如单调系统）外，对安全问题可确定的保护系统知之甚少。因此，我们提出了动态类型访问矩阵（DTAM）模型，该模型通过允许对象的类型动态变化来扩展Sandhu的类型访问矩阵模型。DTAM模型的优点是它可以描述安全问题是可确定的非单调保护系统。特别是，在进一步的限制下，我们可以证明这个问题变得np困难。本文对DTAM模型进行了形式化定义，并对其各个方面进行了深入的讨论。

The safety problem in access matrix models is the one to determine whether or not a given subject can eventually obtain an access privilege to a given object. Generally speaking, unfortunately, the safety problem is undecidable. Little is known about protection systems for which the safety problem is decidable, except for strongly constrained systems (e.g., monotonic systems). Therefore, we propose the Dynamic-Typed Access Matrix (DTAM) Model, which extends Typed Access Matrix model of Sandhu by allowing the type of an object to change dynamically. DTAM model has an advantage that it can describe non-monotonic protection systems for which the safety problem is decidable. Especially, with further restrictions, we can show that the problem becomes NP-hard. In this research we formally define DTAM model and then discuss various aspects of it thoroughly.