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:

Upon completion of this course, the student will be able to do the following:

1. Apply the concepts of standard mathematical logic to produce proofs or refutations of well-formed propositions or arguments phrased in English or in a variety of formal notations (first order logic, discrete mathematics or Hoare logic). Express problems, presented in English, in these formal notations and demonstrate an awareness of the differences between them.
2. Generate a finite state automaton that recognises a given regular language either described in English or presented as a regular expression; similarly, describe the language accepted by a given deterministic or nondeterministic automaton.
3. Relate structural induction to other forms of mathematical induction, and write a recursive definition of a given simple operation on data of a given type presented via an inductive definition of the data structure.
4. Explain the concept of program correctness and prove simple programs correct using Hoare Logic.
5. Demonstrate understanding of Turing Machine computability, and design Turing Machines to accomplish simple tasks.

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.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Propositional Logic.	No practicals.
2	Natural Deduction.	Practicals on Propositional Logic.
3	First Order Logic and Natural Deduction.	Practicals on Natural Deduction.
4	Structural Induction.	Practicals on First Order Logic and Natural Deduction.
5	Hoare Logic – Partial Correctness.	Practicals on Structural Induction.
6	Hoare Logic – Total Correctness.	Practicals on Hoare Logic – Partial Correctness.
7	Deterministic Finite Automata (DFAs).	Practicals on Hoare Logic – Total Correctness.
8	Nondeterministic Finite Automata (NFAs).	Practicals on DFAs.
9	Grammars and Pushdown Automata (PDAs).	Practicals on NFAs.
10	Turing Machines (TMs).	Practicals on Grammars and PDAs.
11	Decidability.	Practicals on TMs.
12	Complexity.	Practicals on Decidability.

Tutorial Registration

Enrollment will be done via Wattle

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment 1 (A1)	10 %	24/08/2022	07/09/2022	1
Assignment 2 (A2)	10 %	30/09/2022	14/10/2022	3,4
Assignment 3 (A3)	10 %	21/10/2022	04/11/2022	2
Quizzes (Q)	10 %	*	*	1,2,3,4,5
Multiple choice exam in Week 5 (W5)	10 %	26/08/2022	29/08/2022	1,3,4
Exam I, mid-semester (E1)	25 %	*	*	1,3,4
Exam II (E2)	25 %	*	*	2,4,5

* 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
• Special Assessment Consideration Guideline and General Information 
• 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)

There will be three exams: a week 5 exam, a mid-term exam and a second exam. The week 5 exam is worth 10% and is redeemable via the mid-semester exam. Exam I (mid-term) is worth 25% of the course. Exam II is worth 25% of the course mark (this is not a final exam).

The final course mark is calculated as max(Default, Redeem), where:

Default = (A1 + A2 + A3)*30% + Q*10% + W5*10% + E1*25% + E2*25%. // ratios as mentioned above

Redeem = (A1 + A2 + A3)*30% + Q*10% + E1*35% + E2*25%. // W5 doesn't count, E1 counts 10% more

A1, A2, A3, Q, W5, E1, E2 are the marks achieved for each assessment item, assuming that all are normalized to 100 points.

Assessment Task 1

Assignment 1 (A1)

Individual assignment, worth 10%. It covers: propositional logic + natural deduction and first order logic + natural deduction.

Assessment Task 2

Assignment 2 (A2)

Individual assignment, worth 10%. It covers: structural induction and Hoare Logic (both partial and total correctness).

Assessment Task 3

Assignment 3 (A3)

Individual assignment, worth 10%. It covers: grammars, DFAs and PDAs.

Assessment Task 4

Quizzes (Q)

• Ten Wattle-based quizzes, worth 1% each. Quizzes will be (almost) weekly, ten times.
• Students will have unlimited attempts for the Wattle quizzes during the time frame.
• A quiz is composed of several questions. Students will get 1 point in a quiz if they answered correctly at least 60% of the questions that composed it, 0 otherwise.
• To make up for any unforeseeable circumstances regarding finishing the quizzes, the final marks for quizzes will be calculated by taking the best 8/10.

Assessment Task 5

Multiple choice exam in Week 5 (W5)

Multiple choice (Wattle-based) exam before census date, worth 10%. It covers: propositional logic+natural deduction, first order logic+natural deduction, structural induction and Hoare logic (syntax and semantics). This exam is redeemable via the mid-semester exam.

Assessment Task 6

Exam I, mid-semester (E1)

Mid-semester exam worth 25%. It covers: propositional logic+natural deduction, first order logic+natural deduction, structural induction and Hoare logic (partial correctness).

Hurdle: students must get a mark of at least 40%.

Assessment Task 7

Exam II (E2)

Exam worth 25%. It covers: Hoare logic (partial and total correctness), grammars, DFAs, PDAs, TMs and computability.

Hurdle: students must get a mark of at least 40%.

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 undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students