Graduation Year

2013

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Mathematics and Statistics

Major Professor

Natasha Jonoska

Keywords

Cellular Automata, Mandatory Results Automata, Symbolic Dynamics, Transducers, Two-Dimensional Languages

Abstract

Models based on various types of automata are ubiquitous in modern science. These models allow reasoning about deep theoretical questions and provide a basis for the development of efficient algorithms to solve related computational problems. This work discusses several types of automata used in such models, including cellular automata and mandatory results automata.

The first part of this work is dedicated to cellular automata. These automata form an important class of discrete dynamical systems widely used to model physical, biological, and chemical processes. Here we discuss a way to study the dynamics of one-dimensional cellular automata through the theory of two-dimensional picture languages. The connection between cellular automata and picture languages stems from the fact that the set of all space-time diagrams of a cellular automaton defines a picture language. We will discuss a hierarchy of cellular automata based on the complexity of the picture languages that they define. In addition to this, we present a characterization of cellular automata that can be described by finite-state transducers.

The second part of this work presents a theory of runtime enforcement based on mech- anism models called Mandatory Results Automata (MRAs). MRAs can monitor and trans- form security-relevant actions and their results. Because previous work could not model general security monitors transforming results, MRAs capture realistic behaviors outside the scope of previous models. MRAs also have a simple but realistic operational seman- tics that makes it straightforward to define concrete MRAs. Moreover, the definitions of policies and enforcement with MRAs are significantly simpler and more expressive than those of previous models. Putting all these features together, we argue that MRAs make good general models of (synchronous) runtime mechanisms, upon which a theory of run- time enforcement can be based. We develop some enforceability theory by characterizing the policies deterministic and nondeterministic MRAs enforce.

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