Model-Based Quantifier Elimination

Lecture 7Nikolaj Bjørner Microsoft ResearchDTU Winter course January 11th 2012Organized by Flemming Nielson & Hanne Riis Nielson

MBQI: MotivationTemplate Based Invariant Generation

If is satisfiable, then post holds

MBQI: Example

If is satisfiable, then post holds

∀ 𝑥 , 𝑦 ,𝑛 . 𝐼 (𝑥 , 𝑦 ,𝑛)∧¬ (𝑥<𝑛)→ 𝑦=2𝑛¿

MBQI: Example

Is satisfiable?Initial model

Then

Iff Iff

is unsat

But it is satisfied with:

∀ 𝑥 , 𝑦 ,𝑛 . 𝐼 (𝑥 , 𝑦 ,𝑛)∧¬ (𝑥<𝑛)→ 𝑦=2𝑛¿

MBQI: Example

MBQI: Example

Idea: Add template macros for I:

Demo