# MAT 361 Finite Automata

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### Course Description

Study of the abstract formalization of digital computers. Applications to computation theory and formal linguistics.

3 units credit.

### Prerequisites

Prerequisite: MAT 281 or equivalent with grade C or better.

### Text

Texts are chosen by the instructor. For example:

Introduction to Computer Theory (2nd ed.), by D. Cohen. Wiley 1997.

### Course Requirements, Tentative Schedule of Class Meetings and Topics, Readings, Assignments and Due dates, Exams

A schedule of class meetings, topics, assignments, due dates, exam dates, etc. will be provided by instructor. See your class syllabus.

Here is an example course outline, based on the above text.

• Sets, relations and functions; proofs;(review material)
• Languages (syntactically defined by various methods)
• Machines (acceptors and transducers, finite state and pushdown automata, Post and Turing machines, determinism)
• Grammars (phrase structure, context free, Chomsky normal form, parsing strings)
• Chomsky hierarchy and examples of each class
• Closure properties (union, complement, product, decision problems)
• Pumping lemmas and the theorems of Kleene, McCarthy, Myhill-Nerode
• Universal Turing machines and the Halting problem

The final exam is given at the date and time announced in the Schedule of Classes.

### Learning Objectives

The purpose of this course is to provide the student with an understanding of what computers (general-purpose symbol manipulating machines) can (and cannot) do; in short the theory of what is computable. In addition (because it turns out to be related to the taxonomy of symbol manipulating machines) a taxonomy of languages is developed.

After completing MAT 361 the student will

1. Define the following terms:
• Language over {a,b}
• Regular language
• Regular expression
• Context free language (CFL)
• Transition graph (TG)
• Deterministic finite state acceptor/automaton (DFSA)
• Nondeterministic finite state acceptor (NDFSA)
• Deterministic pushdown acceptor (DPDA)
• Nondeterministic pushdown acceptor (NPDA)
• Post machine (PM)
• Turing machine (TM)
• Recursive language
• Recursively enumerable (r.e.) language
• Transducer
• Phrase structure grammar
• Regular grammar
• Context free grammar (CFG)
• Chomsky Normal form of a grammar (CNF)
• Universal Turing machine (UTM)
• Chomsky hierarchy of languages
2. State the following:
• Kleene's Theorem
• The pumping lemma for regular languages.
• Myhill-Nerode Theorem
• The pumping lemma for context free languages.
• Turing's hypothesis
• Church's thesis.
• Turing's halting problem
3. Given a language described by any of the following provide a definition of that language using any of the others: DFSA, NFSA, regular expression, regular grammar, TG.
4. Given a language described by either of the following, provide a description using the other: NPDA, CFG.
5. Be able to use the appropriate pumping lemmas and/or the theorem of Myhill-Nerode to prove a language is not regular or is context sensitive.
6. Given a CFG find an equivalent grammar in CNF

### Computers and Calculators, Computer Literacy

Most instructors encourage the use of machines, calculators computers, phones etc., for analyzing data. The use of machines may be restricted during examinations or at certain other times. Ask your instructor for the policy in your class.

Students are not expected to be programmers or to know any particular computer language before starting this class. Some instructors may expect students to be able to access information on the internet, or to use calculators, or to learn to use particular software with instruction. Basic skill in algebra and the use of mathematical symbols, order of operations etc., and the willingness to read and follow instruction manuals and help files will suffice.

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in this course. The instructor determines the relative weights of these factors and the grading scale. See the syllabus for your particular class.

### Location of Class Meetings

Classes meet on the dates and room announced in the official Schedule of Classes. This is a traditional, face-to-face class.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates, Make-Up Work, Missed Exams, and Extra-Credit Assignments

Due dates and policy regarding make-up work and missed exams are set by the instructor. Instructors may, or may not, choose to offer extra credit assignments. If extra credit assignments are offered they will be available to all students.

The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

### Accomodations for Students with Disabilities

Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how we best can help you. All disclosures of disabilities will be kept strictly confidential. Please note: you must register with DSS to arrange an no accommodation. For information call (310) 243-3660 or send an email message to dss@csudh.edu or visit the DSS website http://www4.csudh.edu/dss/contact-us/index or visit their office WH D-180

### Behavioral Expectations

We all are adults so behavior rarely is an issue. Just follow the Golden Rule: "do unto others as you would have them do unto you" then everything will be fine.

The university must maintain a classroom environment that is suitable for learning, so anyone who insists on disrupting that environment will be expelled from the class.

Revision history:

Prepared by C.R. Williams 1/28/00. Revised 7/8/01, 7/25/06, 1/10/15 (G. Jennings).