CS 454, Section 001	Sonoma State University	Spring, 2026

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, some details may be adjusted from semester to semester.
In particular, the Signature Project for this course satisfies SSU's Upper Division GE Area B Requirement for CS Majors, but details of this project likely vary from instructor to instructor and from semester to semester.
In particular,

This course syllabus can be expected to remain stable through the semester (except for clarifying statements or for correcting typographical errors, if any).
The course schedule, assignments, elements of the Signature Project, and other course materials may be adjusted as the semester progresses, until the week before student work is due. Be sure to check/reload Web pages for the course before starting required course work.

Assignment on Undecidability and Reducibility

Proof Summaries: Recall that the Problem 4 of the Assignment on Turing Machines introduced the notion of a proof summary. For this problem, each of the following summaries should be at least 1/2 page.
1. Write a proof summary that outlines the idea behind the proof that the the rational numbers are countable. (Discussion of this result may be found in the textbook.)
2. Write a proof summary that outlines the idea behind the proof of Corollary 4.18 in the text, "Some languages are not Turing-recognizable."
EQ_TM: Write a proof summary for Theorem 5.30. The summary should be at least 2/3 page for the "Turing-recognizable" part of the theorem and at least 2/3 page for the "co-Turing-recognizable" part of the theorem.
Verbose Turing Machines: A Turning Machine is called verbose if it contains one or more states that are never used in the processing of any input string. Formulate the collection of verbose Turing Machines as a language, and show that it is undecidable.
Reducibility of a Decidable Language: Suppose A is a language over an alphabet Σ. Also, suppose L is the infinite language {0^*1^*} With this notation, Exercise 5.23 suggests that A is decidable if and only if A ≤_m L. For this problem, assume that Exercise 5.23 has been proven correct.

With this assumption, rather than consider an infinite language, let w be a given string over alphabet {0, 1}, and let W be the language consisting of the one string w; that is W = {w}.

Is it true that A is decidable if and only if A ≤_m W? Justify your answer.

created Fall, 2023 revised Fall, 2023, January14, 2024
For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.