Browse Theses

The first part of this thesis investigates alternating finite automata (AFA) which is a generalization of nondeterministic finite automata (NFA). AFA (one-way, single-head) are exactly as powerful as deterministic finite automata (DFA) in terms of language recognition. Deterministic and nondeterministic finite automata can be directly constructed from alternating finite automata. Algorithms for transforming a given DFA or an NFA to an equivalent AFA are also given. The boolean operations as well as concatenation and star operations on AFA are also investigated. A type of systems of equations is introduced. Each AFA can be described as such a system of equations. The solutions of such systems are precisely the regular languages. We have explored direct ways of solving such systems of equations and generating regular expressions as the solutions. Normal forms, minimization of AFA, and constructions of equivalent AFA from regular expressions are also studied.The second part is devoted to the relationship between two different models of parallel computation i.e., iterative tree automata (ITA) and alternating Turing machines (ATM). It is shown that ITA and ATM are equivalent in time. More specifically, there is a constant $c$ $>$ 0 such that a language is accepted by a $T(n)$-time ITA if and only if it is accepted by a $cT(n)$-time ATM. It is also shown that any $T(n)$-time ITA can be simulated by uniform boolean circuits of depth $O(T(n)).$ Moreover, $T(n)$-time $d$-dimensional iterative arrays ($d$-IA) can be simulated by ATM in linear time.