Information about the course Automated Reasoning (2IMF25)

This course will be given in the fall of 2015, in the second quartile.
Lectures from 2013 are available on video

Teacher: Prof Dr H. Zantema, Metaforum 6.078, tel 2749,

Students from the Radboud University in Nijmegen that want to follow this course in the fall of 2015 should go to special information for Radboud University in Nijmegen

Obtaining insight how various problems can be transformed to formulas, and can be solved automatically by computer programs manipulating these formulas.

Many problems, in particular in the area of verification of computer systems, can be expressed as proving that some big formula is always true. In this course we will concentrate on various methods for treating this kind of problems. Not only correctness and completeness of these methods will be considered, also efficiency and usability. In particular we will consider:

The examination consists of two parts: a written exam and a practical assignment. The written exam is `closed book': no use of books or notes is permitted during the exam. The practical assignment is done by at most two persons. In case the practical assignment is done by two persons, each of them should be responsible for the whole work, possibly checked by an individual test. The practical assignment has two deadlines: December 7, 2015 for the first part, and January 11, 2016 for the second part.
The reports of the practical assignment should be handed in on paper. This can be done at the lecture, or at the office MF6.078 of the teacher, or in his mail box opposite to room MF6.085.

The results of both parts of the practical assignment (December 2015 and January 2016) and the examination of January 18.

For both the written exam and the practical assignment, the grade should be at least 5.0. In that case the final grade is the average of both parts, each having the same weight. Otherwise the final grade is the minimum of both parts.

To be downloaded:

Some of the material of the course is based on the books:

S. N. Burris:
Logic for Mathematics and Computer Science
Prentice Hall, 1998, ISBN 0-13-285974-2

C. Meinel and T. Theobald:
Algorithms and Data Structures in VLSI Design
Springer, 1998, ISBN 3-540-64486-5

Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein:
Introduction to Algorithms
MIT Press, 2009, ISBN 978-0-262-53305-8
Third Edition, only Chapter 29

Lectures and topics (updated after every lecture; slides refer to version of December 2015):

date topic slides
Monday, November 9 Overview, pigeon hole formula, SAT is NP-complete, arithmetic in SAT 1 to 35
Thursday, November 12 Program correctness by SAT, resolution, Davis-Putnam, completeness 36 to 64
Monday, November 16 DPLL, conflict driven clause learning 65 to 94
Thursday, November 19 Tseitin transformation 95 to 108
Monday, November 23 Linear programming: Simplex method, SMT solving 109 to 138
Thursday, November 26 SMT solving, ILP is NP-hard, unique representation, reachability 139 to 163
Monday, November 30 NuSMV, Decision trees and BDDs 164 to 194
Thursday, December 3 BDDs, predicate logic 195 to 218
Monday, December 7 Predicate logic, resolution, unification 219 to 240
Thursday, December 10 Unification, resolution, Prolog, prenex normal form, Skolemization 241 to 258
Monday, December 14 Prover9, equational reasoning, term rewriting: main properties, termination undecidable 259 to 278
Thursday, December 17 Termination by monotone interpretations and lexicographic path order, well-founded induction 279 to 295
Monday, January 4 Term rewriting: Newman's Lemma, critical pairs, word problem, Knuth-Bendix completion 296 to 317
Thursday, January 7 Critical pairs, overview course, old exam (last lecture) 318

Last change: February 3, 2016