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2023S, VU, 4.0h, 6.0EC

## Properties

• Semester hours: 4.0
• Credits: 6.0
• Type: VU Lecture and Exercise
• Format: Hybrid

## Learning outcomes

After successful completion of the course, students are able to...

- understand, explain and apply Automated Deduction methods, in particular SAT/SMT solving und superposition-based first-order theorem proving.

## Lecture recordings and slides will be posted online on the TUWEL site of the course, and course-related discussions will be monitored online on TUWEL.

The reasoning power that computational logic offers brings new perspectives in the field of program verification. This course is about computational logic, with particular focus on algorithmic and automated methods for proving logical properties.

The course aims at teaching attendees algorithmic techniques and fundamental results in automated deduction. Student will also use state-of-the-art theorem provers for proving logical properties.

## Subject of course

The course focuses on specialised algorithms for reasoning in various fragments of first-order logics, such as propositional logic, combination of ground theories, and full first-order logic with equality. We will address both the theoretical and practical aspects for using and implementing decisions procedures of various logics.

The tentative list of topics covered by the course is below:

• propositional and first-order logic;
• satisfiability checking in propositional logic (splitting, DPLL, randomized algorithms);
• satisfiability checking in the theory of arithmetic, uninterpreted functions and arrays;
• satisfiability checking the the combination of theories (SMT);
• validity proving in first-order logic (superposition theorem proving).

The course will address transformation to normal forms, DPLL, SAT-solving, SMT-solving, resolution, unification, superposition, redundancy checking, and  experiments with theorem provers.

The course will also include hands-on sessions using the SAT solver MINISAT, the SMT solver Z3 and the first-order theorem prover VAMPIRE.

## Teaching methods

There will be two pre-recorded lectures a week, with lecture slides accompanying the lectures.

There will be 4 homeworks,  handed out online.

Exercises/homework solutions, as well as additional, course-related material will be discussed during the in-class discussions.

## Mode of examination

Written

The complete course information (lecture material, news, discussions) is only available on the TUWEL site of the course

The course is held blocked, within 8 weeks, during March 2-May 11, 2023.

The course starts on March 2, 9:15am, with an introductory kick-off lecture summarizing general course information. The kick-off on March 2 is held in-class.

The first proper lecture is on March 7, 9:15-10:45, as a pre-recorded lecture. There will be 2 pre-recorded lectures a week

## Course dates

DayTimeDateLocationDescription
Thu09:00 - 11:0002.03.2023EI 11 Geodäsie HS - GEO LVA Automated Deduction - Kick-off
Thu09:00 - 11:0016.03.2023EI 11 Geodäsie HS - GEO LVA Automated Deduction - QA1
Thu09:00 - 11:0030.03.2023EI 11 Geodäsie HS - GEO LVA Automated Deduction - QA2
Thu09:00 - 11:0027.04.2023EI 11 Geodäsie HS - GEO LVA Automated Deduction - QA3
Thu09:00 - 11:0011.05.2023EI 11 Geodäsie HS - GEO LVA Automated Deduction - QA4
Mon09:00 - 12:0022.05.2023EI 11 Geodäsie HS - GEO Automated Deduction - Written Exam
Mon09:00 - 12:0012.06.2023EI 11 Geodäsie HS - GEO Automated Deduction - Written Exam

## Examination modalities

The course grade will be based on four written homework assignments and a written exam.

Homework assignments count for 40% of the course grade.

The exam will take place as an open-book written exam.

## Course registration

Begin End Deregistration end
06.02.2023 09:00 12.03.2023 23:59 12.03.2023 23:59

## Literature

For slides and other material see the TUWEL course.

English