CSci 423/523 Finite Automata and Theory of Computation
1 Introduction
1.1 Three areas of Theory of Computation
Reading: Sipser 0.1
Theory of Computation is to study the fundamental capabilities and limitations of computers. It contains three areas.
Autom
2 Finite automata
Finite automata are the simplest computational models for computers with an extremely limited amount of memory.
2.1 Examples of nite automata
Reading: Sipser 1.1 (pp. 31-34)
Example: Controller for an automatic door (a sliding door with
7 Non-context-free languages
7.1 Proving non-context-free by pumping lemma
Reading: Sipser 2.3 (pp. 123-127)
Lemma: Consider a parse tree according to a CNF grammar with a yield of w . If the height of the tree is h then
|w| 2h1 .
Theorem (The pumping lem
11 Intractable Problems
Theory of computability is the study of what can or cannot be computed by a TM/computer, among all problems.
Theory of complexity is the study of what can or cannot be computed efciently by a TM/computer, among all
decidable proble
9 Decidability
9.1 Hilberts tenth problem
The Hilberts tenth problem (proposed in 1900 among a list of 23 open problems for the new century): Devise
a process with a nite number of operations that tests whether a polynomial has an integral root. What Hil