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# Decision Procedures

Decision Procedures are the basis for program verification: The task of program verification is to give a formal proof that a program meets its specification. This amounts to determining the truth value of a logical formula. A decision procedure is an algorithm that can for a certain type of formulas decide whether the formula is true or false. We will investigate decision procedures for different logics. Starting with propositional logic we will investigate decision procedures for logics with integers, reals, recursive structures (lists and trees), arrays, etc.
Course type Lecture Andreas Podelski, Jochen Hoenicke, Alexander Nutz Tuesday, 14:00–16:00, Bld. 51, Room 03-026Thursday, 14:00–15:00, Bld. 51, Room 03-026 Thursday, 15:00–16:00, Bld. 51, Room 03-026 Tuesday 20.10.2015 English 6 16.03.2016 here

## News

• (3.2.2016): fixed an error in exercise sheet 13 exercise 3 (Formula was satisfiable), UPDATE (4.2.2016, 2pm):changed exercise 3 again (a bit shorter now)
• (6.1.2016): updated the exam date, the exams will be oral, individual times are still to be assigned
• ATTENTION: The lecture tomorrow (on Tuesday 17.11.) has to be cancelled due to illness.
• update (18.11.2015, 7pm): Lecture and Tutorial on Thursday 19.11.2015 will take place as usual.
• (19.11.2015, 5pm): A new, small exercise sheet is now online, please submit at next Tuesday as normal.

## Formalia

Half of the maximum points from the exercises have to be achieved in order to be admitted for the exam. There will be an exercise sheet each week, usually with three exercises and a maximum of 12 points. You can usually hand in your submission before the lecture on Tuesday -- alone or in groups of two.

### Exam

The exam will be oral or written, depending on the number of participants.

Please register via the examination office as usual.

## Resources

### Textbooks

• Bradley A. R., Manna Z.: The Calculus of Computation: Decision Procedures with Applications to Verification, 2007, Springer, New York.
• Kroening D., Strichmann O.: Decision Procedures - An Algorithmic Point of View, 2008, Springer.

### Papers

• B. Dutertre, L. de Moura: Integrating Simplex with DPLL(T), Technical Report, SRI_CSL-06-01, 2006.
• B. Dutertre, L. de Moura: A fast linear-arithmetic solver for DPLL(T), CAV 2006.

### Tools and Standards

• SMTInterpol  (Interpolating SMT-Solver developed by us --- the chair of software engineering)
• CVC4 (SMT-Solver developed by New York University and the University of Iowa)
• Yices (SMT-Solver developed by Stanford Research Institute)
• Z3 (SMT-Solver developed by Microsoft Research)
• SMTLIB (A standard for encoding SMT-problems which is read by many solvers)