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 Algorithm Complexity and Class P

  1. Definitions: Consider the terms, "Class P", "decidable", "undecidable", "recognizable", "non-recognizble".
    Give careful definitions of each of these terms.

  2. Class P Problems: Identify 3 problems in Class P, and explain why each is in Class P.

  3. Class P and Searching in a Balanced Binary Search Tree: Searching for an element in a balanced binary search tree with n nodes has O(log n). Since log n is a mathematical function that is not a polynomial, is it correct to conclude that the problem of searching for an element in a balanced binary search tree is NOT in Class P? Justify your answer.

  4. Class P and Mapping Reducibility: Suppose A and B are problems, and C is a problem in Class P.

    1. If A ≤M C, does it follow that A is in Class P? Justify your conclusion.
    2. If C ≤M B, does it follow that B is in Class P? Justify your conclusion.

  5. Relationships Among Languages: Suppose S and T are two languages in Class P.

    1. Let I be the intersection of the strings in S and T. Is I always, sometimes, or never in Class P? Explain.
    2. Is the concatenated language ST always, sometimes, or never in Class P? Explain.
    3. Is the complement of S in Class P always, sometimes, or never? Explain.
    4. Let U be the union of the strings in S and T. Is it always the case that U must be in Class P? Is U sometimes in Class P and sometimes not? Is U never in Class P? Explain.

    In each case, justify your answer.

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