On the descriptional complexity of iterative arrays

The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable

Security Applications of Formal Language Theory

We present an approach to improving the security of complex, composed systems based on formal language theory, and show how this approach leads to advances in input validation, security modeling, attack surface reduction, and ultimately, software design and programming methodology. We cite examples based on real-world security flaws in common protocols representing different classes of protocol complexity. We also introduce a formalization of an exploit development technique, the parse tree differential attack, made possible by our conception of the role of formal grammars in security. These insights make possible future advances in software auditing techniques applicable to static and dynamic binary analysis, fuzzing, and general reverse-engineering and exploit development. Our work provides a foundation for verifying critical implementation components with considerably less burden to developers than is offered by the current state of the art. It additionally offers a rich basis for further exploration in the areas of offensive analysis and, conversely, automated defense tools and techniques. This report is divided into two parts. In Part I we address the formalisms and their applications; in Part II we discuss the general implications and recommendations for protocol and software design that follow from our formal analysis

Descriptional complexity of cellular automata and decidability questions

We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata