Date of Graduation
Statler College of Engineering and Mineral Resources
Lane Department of Computer Science and Electrical Engineering
In this thesis, we analyze the problem of state minimization in 2-MDFAs. The class of 2-MDFAs is an extension of the class of DFAs, allowing a small amount of nondeterminism; specifically two start states. Since nondeterminism allows finite automata to be more succinct, it is worthwhile to investigate the problem of minimizing such finite automata. In the case of unbounded non-determinism, i.e., NFAs, such automata can be exponentially more succinct than DFAs , but the corresponding minimization problem is PSPACE-complete . Even in the case of 2-MDFAs, which are only polynomially more succinct than DFAs, the minimization problem remains non-trivial; indeed,  shows that the corresponding decision problem is NP-complete. We are concerned with the approximability of the 2-MDFA minimization problem. Our main contribution in the current work is the design of an n-factor approximation algorithm for state minimization in 2-MDFAs.
Tauras, Chris, "State minimization problems in finite state automata" (2007). Graduate Theses, Dissertations, and Problem Reports. 2541.