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 Class NP and NP-Completeness

Definitions: Consider the terms, "Class NP", "verifier for a language", and "NP-complete".
Give careful definitions of each of these terms.
A Permutation Sort: One approach for sorting an array of n elements is to generate all n! permutations of the elements and then each is examined to determine which permutation is ordered.
1. Explain why this algorithm, called a Permutation Sort, has Θ(n * n!).
2. Since n * n! is not a polynomial, must we conclude that sorting is not in Class P? Explain briefly.
3. Does this or another analysis prove that sorting is in Class NP? Explain.
Tree Traversals: Consider an [in-order] traversal of a binary search tree with n nodes.
1. Does this algorithms demonstrate that the problem of traversing a graph is in Class P? Explain.
2. Does this algorithms demonstrate that the problem of traversing a graph is in Class NP? Explain.
Satisfiability and NP-Completeness: Suppose A and B are problems in class NP.
1. Recall that the Problem 4 of the Assignment on Turing Machines introduced the notion of a proof summary. Write a proof summary that outlines the idea behind the proof that the Satisfiability Problem (SAT) is NP-Complete.
2. If A ≤_M SAT, does it follow that A is NP-Complete? Justify your conclusion.
3. If SAT ≤_M B, does it follow that B is NP-Complete? Justify your conclusion.
NP-Complete and NP-Hard: Consider the concepts of a NP-Hard problem and an NP-Complete problem.
1. Can a problem be NP-Hard without being NP-Complete? Explain.
2. Can a problem be NP-Complete without being NP-Hard? Explain.

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