Some theoretical aspects of verification (with a focus on bisimilarity)
Some theoretical aspects of verification (with a focus on bisimilarity)
Some theoretical aspects of verification (with a focus on bisimilarity)
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Questi<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> completeness and (algorithmic) decidability<br />
Kurt Gödel (1906-1978)<br />
in 1930 completeness (Γ ⊢ φ iff Γ |= φ)<br />
(Every c<strong>on</strong>sistent 1st order theory has a model.)<br />
Presburger arithmetic (theory <str<strong>on</strong>g>of</str<strong>on</strong>g> additi<strong>on</strong>; symbols 0, 1, + [and =])<br />
1. ∀x : ¬(0 = x + 1)<br />
2. ∀x∀y : ¬(x = y) ⇒ ¬(x + 1 = y + 1)<br />
3. ∀x : x + 0 = x<br />
4. ∀x∀y : (x + y) + 1 = x + (y + 1)<br />
5. An axiom scheme:<br />
(P(0) ∧ ∀x : P(x) ⇒ P(x + 1)) ⇒ ∀x : P(x)<br />
P(x) ... any formula c<strong>on</strong>structed from 0, 1, +, =<br />
and c<strong>on</strong>taining a single free variable x<br />
Petr Jančar (TU Ostrava) <str<strong>on</strong>g>Some</str<strong>on</strong>g> <str<strong>on</strong>g>aspects</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>verificati<strong>on</strong></str<strong>on</strong>g><br />
Kolloquium Jena, 14 May 2007 10 /<br />
89
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