CS 454, Section 001	Sonoma State University	Spring, 2024

Theory of Computation
Instructor: Henry M. Walker Lecturer, Sonoma State University Professor Emeritus of Computer Science and Mathematics, Grinnell College

Although much of this course has been well developed in recent semesters, the SSU CS faculty recently have approved an updated course description. Also, the required SSU Signature Project for SSU's Upper Division GE Area B Requirement for CS Majors has been rethought for this course. Currently, the Web site is reasonably stable, but modest refinements are likely. Check these pages regularly for adjustments.

Contract Negotiations Have Yielded a Tentative Agreement

Since May, 2024, the California Faculty Association (CFA) – the labor union of professors, lecturers, librarians, counselors, and coaches across the 23 California State University campuses – has been in negotiations with the management of the California State University System. After a one-day strike on Monday, January 22, the two sides have reached a tentative agreement, and the strike has been called off. Effective Tuesday, January 23, SSU classes (including CS 454) will be held as scheduled.

Assignment on Turing Machines

Turing Machine for 2 a's: Consider an input alphabet Σ = {a, b}, and let L = {strings w over Σ | w contains two consecutive a's}. Design a Turing machine that accepts the language L. Write out your machine in full, both using a complete transition table and using a state diagram.

Consider the input alphabet for this problem to be {a, b}.
Turing Machine for Palindromes: Design a Turing machine that reads a string s and returns the string ss^R, where s^R is the reverse of the string s. For example, given the string "abbaa", the Turing machine should halt after "abbaaaabba" is printed on the tape. As in Problem 1, write out your machine in full, both using a complete transition table and using a state diagram, and consider the input alphabet to be {a, b}.
Derivations of Context Free Grammars in Chomsky Normal Form:
1. Suppose G is a context free grammar in Chomsky Normal Form, and suppose s is a string of length k that is generated by G. Show that the derivation of s will require exactly 2k-1 steps.
2. Give an example to illustrate why a proof of part a by mathematical induction might be extremely difficult, if not impossible.
Proof Summaries: Behind the proof of each theorem lies an idea. The details of a proof may require extensive exposition, but the underlying idea often can be explained in several sentences. For each of the following theorems, write an explanation (in your own words) of why the result is true; what is/are the main idea(s) of the proof.
1. Theorem 3.13
2. Theorem 3.16
Notes:
- Since your proof summaries are to be in your own words, it is not acceptable to copy a proof from the text, just changing a few words now and then. Think about how to reorganize the proof or how to present in at a different level of detail (e.g., explaining the main ideas, but leaving out selected details that simply implement the main ideas).
- Each explanation should be reasonably thorough — 1/2-2/3 page in length for each part.
- Each explanation should include all main ideas of the argument; details may be omitted, but only if they follow naturally from the ideas presented.
- Each explanation should be logically organized and clearly written.

created Fall, 2023 revised Fall, 2023
For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.