By Jacques Duparc, Thomas A. Henzinger

ISBN-10: 3540749144

ISBN-13: 9783540749141

The 36 revised complete papers provided including the abstracts of 6 invited lectures have been conscientiously reviewed and chosen from 116 submissions. The papers are prepared in topical sections on good judgment and video games, expressiveness, video games and timber, common sense and deduction, lambda calculus, finite version idea, linear common sense, evidence concept, and online game semantics.

**Read Online or Download Computer Science Logic: 21 International Workshop, CSL 2007, 16th Annual Conference of the EACSL, Lausanne, Switzerland, September 11-15, 2007, Proceedings PDF**

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**Extra info for Computer Science Logic: 21 International Workshop, CSL 2007, 16th Annual Conference of the EACSL, Lausanne, Switzerland, September 11-15, 2007, Proceedings**

**Sample text**

Thus, x can be determined by solving the appropriate LP. In the example, this results in the vector x = (3, 0). ∞. If this is not the case, the LP In general, it might not be the case that μ∗ corresponding to the system E is not feasible. t. xj → xi iff xi = −∞ and −∞ does not occur as a constant in E, ei ∈ E and xj occurs in ei . Since μ∗ [[e]]μ∗ > −∞ for every subexpression occurring in E. Thus, μ∗ (xj ) = ∞ and xj →∗ xi implies μ∗ (xi ) = ∞. In particular if μ∗ (xi ) = ∞ for some variable xi of a strongly connected component (SCC), then μ∗ (xj ) = ∞ for every variable xj of the same SCC.

We find: Lemma 10. Assume that E denotes a conjunctive system with LP which uses n variables and m ∨-expressions. Algorithm 1 computes at most n · Π(m + n) times the least solution μ of E(π) with μ ≥ μ for some π and some LP-consistent pre-solution μ of E(π). After that, it returns the least solution of E. We want to compute the least solution μ of E with μ ≥ μ which is also the least solution of [E] with μ ≥ μ. Recall from section 3 that for this purpose we essentially have to compute least consistent solutions of feasible systems of conjunctive equations.

Assume that E denotes a conjunctive system with n variables. Let (μi )i∈N denote an increasing sequence of consistent pre-solutions of E. Let μi denote the least solution of E with μi ≥ μi for i ∈ N. Then |{μi | i ∈ N}| ≤ n. We now use the results above in order to compute the least consistent solution μ∗ of the ∞. feasible conjunctive system E. We first restrict our consideration to the case μ∗ Since, by lemma 5, μ∗ is the only solution of E with μ ≤ μ∗ ∞, μ∗ is in particular the greatest solution of E with μ∗ ∞.

### Computer Science Logic: 21 International Workshop, CSL 2007, 16th Annual Conference of the EACSL, Lausanne, Switzerland, September 11-15, 2007, Proceedings by Jacques Duparc, Thomas A. Henzinger

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