Computational Logic and Proof Theory: 5th Kurt Gödel by Leo Bachmair (auth.), Georg Gottlob, Alexander Leitsch,

By Leo Bachmair (auth.), Georg Gottlob, Alexander Leitsch, Daniele Mundici (eds.)

This e-book constitutes the refereed court cases of the fifth Kurt Gödel Colloquium on Computational common sense and facts idea, KGC '97, held in Vienna, Austria, in August 1997.
The quantity offers 20 revised complete papers chosen from 38 submitted papers. additionally incorporated are seven invited contributions via prime specialists within the zone. The booklet files interdisciplinary paintings performed within the region of machine technology and mathematical logics by means of combining learn on provability, research of proofs, evidence seek, and complexity.

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Additional resources for Computational Logic and Proof Theory: 5th Kurt Gödel Colloquium, KGC '97 Vienna, Austria, August 25–29, 1997 Proceedings

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A Do A D00 A A D0~ A Fig. 1. This figure illustrates the balancing of the conjunction computing C~,a[u, v]. The Dw's are intended to be replaced by inputs D~a[uw , v], although these are relevant only for Iwl >_ 2; and the above circuit is intended only to illustrate the idea of the construction of the conjunction. [] 4 An Alogtime Algorithm for Tree Comparison In the next two sections, we give Alogtime algorithms for the tree comparison and tree canonization problems. We'll start with the tree comparison problem, and then see that a solution to the tree comparison problem can be used to give a solution to the tree canonization problem.

ULLMAN, The Design and Analysis of Computer Algorithms, Addison-Wesley~ 1974. 2. D. i . I~. BARRINGTON, Bounded-width polynomial-size branching programs recognize exactly those languages in N C 1, J. Comput. , 38 (1989), pp. 150-164. 3. S. R. Buss, The Boolean formula value problem is in ALOGTIME, in Proceedings of the 19-th Annual ACM Symposium on Theory of Computing, May 1987, pp. 123-131. 33 4. - - , Algorithms for Boolean formula evaluation and for tree contraction, in Arithmetic, Proof Theory and Computational Complexity, P.

The gate Dl,a[uw, v] outputs True provided that the number of trinary strings x in 2i{0, 1}~+2 with lxl = [wI for which Ct+~[uw,vx] = True is equal to the number for which C~l[UW, ux] = True, There are 3 twl many trinary strings x e {0, 1, 2}lwl; therefore, using the Alogtime circuits for counting, the gate Dl,a[uw, v] can be computed by a circuit of depth O(twl) which has as inputs the gates The description of the circuit gn is now complete, since the output of g~ is just the gate C~2[e , el. There are a couple things which must be verified to see that g~ is a correct, logarithmic depth circuit.

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