With the rapid growth in wireless networks and sensor and mobile devices, we are moving towards an era of pervasive computing. Access control is challenging in these environments. In this work, we propose a trust based approach for access control for pervasive computing systems. Our previously proposed belief based trust model is used to evaluate the trustworthiness of users. Fine-grained access control is achieved depending on the trust levels of users. We develop a class of trust-based access control models having very formal semantics, expressed in graph theory. The models differ with respect to the features they provide, and the types of the trust constraints that they can support.