By Bruno Buchberger (auth.), Ulrich Furbach, Natarajan Shankar (eds.)
This booklet constitutes the refereed complaints of the 3rd overseas Joint convention on computerized Reasoning, IJCAR 2006, held in Seattle, WA, united states in August 2006 as a part of the 4th Federated good judgment convention, FLoC 2006. IJCAR 2006 is a merger of CADE, FroCoS, FTP, TABLEAUX, and TPHOLs.
The forty-one revised complete study papers and eight revised approach descriptions awarded including three invited papers and a precis of a structures pageant have been rigorously reviewed and chosen from a complete of 152 submissions. The papers tackle the full spectrum of study in automatic reasoning together with formalization of arithmetic, evidence idea, evidence seek, description logics, interactive evidence checking, higher-order good judgment, blend equipment, satisfiability methods, and rewriting. The papers are equipped in topical sections on proofs, seek, higher-order good judgment, evidence idea, seek, evidence checking, mix, choice tactics, CASC-J3, rewriting, and outline logic.
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Extra info for Automated Reasoning: Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20, 2006. Proceedings
After 4 years of refereeing by a team of 12 referees, an abridged version was published only recently . The referees declared that they were 99% certain of the correctness of the proof. The programs were merely given a “diagonal look”. edu/∼thales/ﬂyspeck) to formalize the whole proof with a theorem prover. This paper is the ﬁrst deﬁnite contribution to ﬂyspeck. Hales’ proof goes roughly like this: any potential counter example (denser packing) gives rise to a tame plane graph, where tameness is a very speciﬁc notion; enumerate all (ﬁnitely many) tame graphs (by computer); for each of them check (again by computer) that it cannot constitute a counter example.
A graph is tame if it is plane and satisﬁes 8 conditions: 1. The size of each face is at least 3 and at most 8: tame 1 g ≡ ∀ f ∈F g. 3 ≤ |vertices f | ∧ |vertices f | ≤ 8 2. Every 3-cycle is a face or the opposite of a face: tame 2 g ≡ ∀ a b c. is-cycle g [a, b, c] ∧ distinct [a, b, c] −→ (∃ f ∈F g. vertices f ∼ = [a, b, c] ∨ vertices f ∼ = [c, b, a]) where is-cycle g vs ≡ hd vs ∈ set (neighbors g (last vs)) ∧ is-path g vs, function neighbors does the obvious and is-path g  = True is-path g (u · vs) = (case vs of  ⇒ True | v · ws ⇒ v ∈ set (neighbors g u) ∧ is-path g vs) 3.
3) that same (tameEnum 0 800000 ) Tri, same (tameEnum 1 8000000 ) Quad, same (tameEnum 2 20000000 ) Pent, same (tameEnum 3 4000000 ) Hex, same (tameEnum 4 1000000 ) Hept, and same (tameEnum 5 2000000 ) Oct, where same is an executable check of equivalence (modulo )3 of two lists of fgraphs. Corollary fgraph ‘ TameEnum ⊆ Archive follows by correctness of tameEnum (Theorem 4) . We cannot detail the deﬁnition of same (or its correctness theorem) but we should point out that it is a potential bottleneck: for p = 2 we need to check 15000 graphs for inclusion in an archive of 1500 graphs — modulo graph isomorphism!
Automated Reasoning: Third International Joint Conference, IJCAR 2006, Seattle, WA, USA, August 17-20, 2006. Proceedings by Bruno Buchberger (auth.), Ulrich Furbach, Natarajan Shankar (eds.)