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SC Chapter 5 SMT Solving

Questions about the lecture 'Satisfiability Checking' of the RWTH Aachen Chapter 5 SMT Solving

Questions about the lecture 'Satisfiability Checking' of the RWTH Aachen Chapter 5 SMT Solving


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What is the definition of SMT Solving?

Expand propositional logic with theories extending SAT to SAT-modulo-theories (SMT)

What is provided by the SMT community? [3]

1. SMT-LIB exists with language benchmarks tutorials

2. SMT-COMP exists with measuring performance and capabilities of tools

3. SMT workshops are held annually

What is the idea behind the eager approach of SMT? [2]

1. First theory and then SAT solver

2. Transformation of all NP-complete problems with polynomial effort to equivalent SAT problems // Not always most effective

What is the idea behind the full lazy approach of SMT?

First SAT solver and then theory

What are current implementations? [10]

1. UCLID

2. STP

3. Spear

4. Boolector

5. Beaver

6. SONOLAR

7. SWORD

8. CVC3

9. MathSAT

10. Z3

What is the definition of equality logic with uninterpreted functions? [6]

1. Propositional with equalities (P) and uninterpreted functions (F)

2. Both are NP-complete thus they model same decision problems

3. Input in NNF

 

4. Formula of propositional logic is phi^B

5. Formula with equalities is phi^E

6. Formula with equalities and uninterpreted functions is phi^UF

What is the effort of the removing constants algorithm in SMT?

Algorithm for phiUF in polynomial time

What is the idea of reducing phiUF to phiE? [2]

1. Replace f(a) by xf(a)

2. Assume that for all a,b in Dn that f(a)!=f(b) → a!=b