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 Undecidability and Reducibility

  1. 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."

  2. EQTM: 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.

  3. 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.

  4. 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.

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