This course presents some formal notations that are commonly used for the description of computation and of computing systems, for the specification of software and for mathematically rigorous arguments about program properties. The following areas of study constitute the backbone of the course. Predicate calculus and natural deduction, inductive definitions of data types as a basis for recursive functions and structural induction, formal language theory (particularly regular expressions, finite state machines and context-free grammars), and specification languages.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Apply the concepts of mathematical logic to formulate assertions and construct proofs or refutations in a variety of formalisms.
2. Prove simple properties of recursive functions on inductively defined data structures using structural induction.
3. Prove simple programs correct using Hoare Logic.
4. Understand, analyse, and describe formal languages in a variety of representations including grammars and automata and Turing machines.
5. Apply standard concepts of computability and complexity theory to classify computational problems.

Research-Led Teaching

The course covers the fundamentals of theoretical computer science and can directly lead to applications in research.

Field Trips

n/a

Additional Course Costs

n/a

Examination Material or equipment

n/a

Required Resources

n/a

Recommended Resources

[1] Winfried Karl Grassmann and Jean-Paul Tremblay. 1996. Logic and Discrete Mathematics: A Computer Science Perspective. Prentice Hall Press, Upper Saddle River, NJ, USA.

[2] Willem Conradie, Valentin Goranko and Claudette Robinson. 2015. Logic and Discrete Mathematics: a concise Introduction. Chichester, West Sussex, United Kingdom : Wiley. (Available online via the ANU library.)

[3] Susanna S. Epp. 2010. Discrete Mathematics with Applications. Brooks/Cole Publishing Co., Pacific Grove, CA, USA. (Available online via the ANU library.)

[4] David J. Hunter. 2010. Essentials of Discrete Mathematics (2nd ed.). Jones and Bartlett Publishers, Inc., USA. (Available online via the ANU library.)

[5] Harris Kwong. 2015. A Spiral Workbook for Discrete Mathematics. Amazon Digital Services LLC. (Available online here.)

[6] John E. Hopcroft, Rajeev Motwani, and Jeffrey D. Ullman. 2006. Introduction to Automata Theory, Languages, and Computation (3rd Edition). Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA. (Available online via the ANU library.)

[7] Martin D. Davis, Ron Sigal, and Elaine J. Weyuker. 1994. Computability, Complexity, and Languages (2nd Ed.): Fundamentals of Theoretical Computer Science. Academic Press Prof., Inc., San Diego, CA, USA.

[8] Benjamin C. Pierce, Arthur Azevedo de Amorim, Chris Casinghino, Marco Gaboardi, Michael Greenberg, Catalin Hritcu, Vilhelm Sjöberg, Andrew Tolmach, and Brent Yorgey. 2018. Programming Language Foundations. Software Foundations series, volume 2. Electronic textbook. (Available here (volume 2).)

[9] Gordon, “Specification and Verification I”, online.

[10] C. A. R. Hoare. 1969. An axiomatic basis for computer programming. Commun. ACM 12, 10 (October 1969), 576-580. DOI=http://dx.doi.org/10.1145/363235.363259. (Available here.)

[11] Floyd, R. W. 1967. Assigning Meanings to Programs. Proceedings of Symposium on Applied Mathematics, 19, 19-32. (Available here.)

Staff Feedback

Students will be given feedback in the following forms in this course:

• written comments
• verbal comments
• feedback to whole class, groups, individuals, focus group etc.

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Other Information

Gen AI Toolsare NOT ALLOWED: 

“This course introduces fundamental concepts that could potentially be addressed by certain Generative AI tools (e.g., ChatGPT). Hence, the use of any Generative AI tools is not permitted in graded assessments within this course.”  

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Propositional Logic.	No Practicals.
2	Reasoning about Functional Programs.	Practicals on Basic Reasoning.
3	Reasoning about Inductive Types (Natural Numbers and Lists).	Practicals on Inductive Types.
4	Reasoning about General Inductive Types (Trees and others).	Practicals on More Complex Inductive Types.
5	Reasoning about Imperative Programs / Partial Correctness.	Practicals on Imperative Programs / Partial Correctness.
6	Reasoning about Imperative Programs / Total Correctness.	Practicals on Imperative Programs / Total Correctness.
7	Deterministic Finite Automata (DFAs).	Practicals on DFAs.
8	Nondeterministic Finite Automata (NFAs).	Practicals on NFAs.
9	Grammars and Pushdown Automata (PDAs).	Practicals on Grammars and PDAs.
10	Turing Machines (TMs).	Practicals on TMs.
11	Decidability.	Practicals on Decidability.
12	Complexity.	Practicals on Complexity.

Tutorial Registration

Students choose their tutorials via MyTimetable.

Assessment Summary

Assessment task	Value	Learning Outcomes
Mini-Assignments	40 %	1,2,3,4,5
Quizzes	10 %	1,2,3,4,5
Final exam	50 %	1,2,3,4,5

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines , which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Skills website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Examination(s)

The course includes a formal examination. This is assessment item 3.

Assessment Task 1

Mini-Assignments

Mini-Assignments will be distributed in lecture weeks 2 -- 11 inclusive and are due the following week, and are returned one week after submission. Each mini-assignment is worth 4 marks so that assignments in total are worth 40% of the overall mark.

Assessment Task 2

Quizzes

There will be five quizzes, each covering approximately two weeks of course material. Quizzes are on Wattle, and each quiz will be worth 2 marks so that the quiz total is 10% of the overall mark. The quizzes are auto-marked and marks will be returned once the quiz closes, or at most 5 working days after the closing of the quiz in case of extension requests.

Assessment Task 3

Final exam

Final exam worth 50 marks. This is a hurdle exam and course participants must score a mark of at least 40 to pass the course.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records.

All submissions will be via Wattle.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

Late submission of assessment items is not permitted without an extension requested in writing on or before the due date. A mark of 0 will be awarded for late submission.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material.

Returning Assignments

Assignment marks and feedback will be given online.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

Resubmission of assignments will not be permitted without grant of Special Consideration.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Access and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents all ANU students