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 Algorithm Complexity and Class P

Definitions: Consider the terms, "Class P", "decidable", "undecidable", "recognizable", "non-recognizble".
Give careful definitions of each of these terms.
Class P Problems: Identify 3 problems in Class P, and explain why each is in Class P.
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.
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.
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.

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