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 DFAs/NFAs and Regular/Non-regular Expressions

A Regular Expression and Its Corresponding NFA

Consider the regular expression ( (1 1^* 00 )^* ) ∪ 01^*.
1. Identify two strings that are members of the language described by this regular expression.
2. Identify two strings that are NOT members of the language described by this regular expression.
3. Use the procedure described in Lemma 1.55 to covert the above regular expression to an NFA.

Regular and Non-regular Languages

For each of the following, determine if the language is regular or not, and justify your answer in each case.
1. Let the alphabet Σ = {0, 1, +, =} and let A be the language: A = {x=y+z | x, y, and z are binary unsigned integers and x is the sum of y and z} Is A an regular language? Justify your answer.
2. Let the alphabet Σ = {a, b}, and let B be the strings over this alphabet with either an even number of a's or an odd number of b's, but not both an even number of a's and an odd number of b's. Is B a regular language? Justify your answer.
3. Consider the alphabet Σ = {a, b}. For a string s ∈ Σ^*, define s^R as the reverse of s. That is, the characters in s^R are the same as the characters in s, but the characters appear in the reverse order. Is {s s^R | s ∈ Σ^*} a regular language? Be sure to justify your answer.

DFA-based/Table-driven Program

Recognizing Numbers Although C/C++ allow several different formats for numbers, this problem considers only two main forms.
- Integers
  - An integer is a sequence of one or more digits {0, 1, . . . 9}.
  - For an integer, the digit sequence may (or may not) be preceded by a single plus (+) or minus (-) sign.
  - An integer may not contain a period or any non-digit character (except for a possible + or - character at the start).
- Floating-point numbers
  - A floating-point number is a sequence of one or more digits (0, 1, 2, . . . 9}, with exactly one period inserted at some position (e.g., at the start, the end, or somewhere between the ends.
  - For a floating-point number, the digit/period sequence may be preceded by a single plus (+) or minus (-) sign.
  - No other characters are permitted within a floating-point number.
Notes: For this problem:
- Integers may begin with any number of zeros, but an initial zero is not required..
- Floating-point numbers must contain a period, but the period may or may not be preceded by a digit.
- Both integers and floating-point numbers may contain any number of digits; the overall magnitude of the number or the number of digits is irrelevant to the specification of these numbers.
- A period character, by itself, is not a floating-point number.
- In parts a and b that follow, use the symbol D to represent any digit in the set {0, 1, 2, . . . 9}.—in the interests of simplicity of writing, you need not use each separate decimal digit in your state diagrams, unless you find that necessary.
1. Write a DFA to recognize both integers and floating-point numbers, as defined above.
  When scanning characters to identify a number, find the longest sequence of characters that can be a number.
  Thus, 123.456 should be identified as a floating-point number, not the integer 123 , following by the floating-point number .456 .
  Similarly, 123.45.6789 should be identified as the floating-point number 123.45 , followed by the floating point number .6789 .
2. Write a regular expression to accept all strings that are either integers or floating-point numbers, as defined above.
3. Using either the program dfa-comments.c or or the template dfa-comments-2.c as an example, write a DFA-based/table-driven program that uses your DFA of part a to identify and print all numbers read (until an end-of-file character is encountered). For each number identified, the program should label it appropriately as an integer or floating point type.
  As with all programs for this course,
  - The program must conform to the SSU CS C/C++ Style Guide.
  - For this problem, submit both a listing of the C/C++ program, and a description of test runs, and the corresponding results.
  - If you use a file in testing, print and submit the contents of the file.

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