# Computer Aided Verification: 11th International Conference, by David L. Dill (auth.), Nicolas Halbwachs, Doron Peled (eds.)

By David L. Dill (auth.), Nicolas Halbwachs, Doron Peled (eds.)

This ebook constitutes the refereed complaints of the eleventh foreign convention on machine Aided Verification, CAV'99, held in Trento, Italy in July 1999 as a part of FLoC'99.

The 34 revised complete papers offered have been conscientiously reviewed and chosen from a complete of 107 submissions. additionally integrated are six invited contributions and 5 device shows. The e-book is geared up in topical sections on processor verification, protocol verification and trying out, endless country areas, idea of verification, linear temporal common sense, modeling of structures, symbolic version checking, theorem proving, automata-theoretic tools, and abstraction.

**Read or Download Computer Aided Verification: 11th International Conference, CAV’99 Trento, Italy, July 6–10, 1999 Proceedings PDF**

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**Extra resources for Computer Aided Verification: 11th International Conference, CAV’99 Trento, Italy, July 6–10, 1999 Proceedings**

**Sample text**

In particular, under such interpretation ∗, the probability of X ∗ , if deﬁned, is at least P (t∗ ). t. the aforementioned set-theoretical/probabilistic interpretation: all theorems of PE hold at each outcome from Ω. On Aggregating Probabilistic Evidence 35 Theorem 1 (Soundness with Respect to Probabilistic Semantics). Logical entailment yields probabilistic entailment: Γ F ⇒ Γ F. Proof. Induction on derivations in Γ . If F is an axiom of PE, then, by Proposition 1, F ∗ = Ω and hence Γ ∗ ⊆ F ∗ .

A similar observation shows that if the probability of all propositions from Γ is 1, then the probability of X is also 1. But what happens in a general case when formulas from Γ have arbitrary probabilities? Does logical entailment (1) yield meaningful estimates of the probability of X? c Springer International Publishing Switzerland 2016 S. Artemov and A. ): LFCS 2016, LNCS 9537, pp. 27–42, 2016. 1007/978-3-319-27683-0 3 28 S. Artemov The aforementioned logical observation “X is true whenever Γ is true” yields an estimate: X holds on the intersection of all events Fi , i = 1, 2, .

Furthermore, t∗ = Ω as well, and (t:X)∗ = ∅, which means that u:Γ The following Corollary 2 shows that for each Γ and X, the approximation provided by aggregated evidence AE Γ (X) cannot be improved uniformly for all probability spaces. Corollary 2. u:Γ t:X ⇔ t AE Γ (X). Proof. , t is evidence for X in any probabilistic model of Γ . Now let u:Γ t:X. By Theorem 3, u:Γ t:X, hence, by Corollary 1, t AE Γ (X). 1 General Picture Model-Theoretical View To build the aggregated evidence term AE Γ (X), ﬁnd all (set-theoretically minimal) subsets Γ of Γ such that Γ |= X and form lattice products ui1 ui2 .