Download Abstraction, Reformulation, and Approximation: 4th by Patrick Cousot (auth.), Berthe Y. Choueiry, Toby Walsh PDF

By Patrick Cousot (auth.), Berthe Y. Choueiry, Toby Walsh (eds.)

This quantity comprises the lawsuits of SARA 2000, the fourth Symposium on Abstraction, Reformulations, and Approximation (SARA). The convention used to be held at Horseshoe Bay lodge and convention membership, Lake LBJ, Texas, July 26– 29, 2000, simply sooner than the AAAI 2000 convention in Austin. past SARA meetings happened at Jackson gap in Wyoming (1994), Ville d’Est´erel in Qu´ebec (1995), and Asilomar in California (1998). The symposium grewout of a chain of workshops on abstraction, approximation, and reformulation that had taken position along AAAI because 1989. This year’s symposium used to be truly scheduled to occur at Lago Vista golf equipment & lodge on Lake Travis yet, end result of the resort’s failure to pay taxes, the convention needed to be moved past due within the day. This mischance engendered eleventh-hour reformulations, abstractions, and source re-allocations of its personal. Such are the perils of organizing a convention. this is often the ?rst SARA for which the lawsuits were released within the LNAI sequence of Springer-Verlag. we are hoping that this can be a re?ection of the elevated adulthood of the ?eld and that the elevated visibility introduced through the ebook of this quantity can assist the self-discipline develop even extra. Abstractions, reformulations, and approximations (AR&A) have stumbled on - plications in various disciplines and difficulties together with automated progr- ming, constraint delight, layout, prognosis, desktop studying, making plans, qu- itative reasoning, scheduling, source allocation, and theorem proving. The - pers during this quantity trap a cross-section of those software domains.

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Example text

This decomposes the overall task (root) into two subtasks: get the passenger (move the taxi to the passenger’s location and pick up the passenger), and put the passenger (move the taxi to the passenger’s destination and put down the passenger). Each of these is decomposed in turn. get decomposes into navigate(source) and the primitive pickup, while put decomposes into navigate(destination) and the primitive putdown. Finally, the parameterized subroutine navigate(t) decomposes into the four motion primitives north, south, east, and west.

For example, there is no need to represent C(root, s, put) in states where the passenger is not in the taxi, because the put is terminated in such states. Another structural constraint concerns implication relationships between a child task and its parent task. In some states, the termination predicate of the child task implies the termination predicate of the parent task. In such states, 38 Thomas G. Dietterich the completion cost must be zero. For example, C(root, s, put) is always zero in cases where the put is not terminated, because after the put is completed, the passenger will be at his/her destination, and therefore, the root task will be terminated as well.

Theorem 27. Under Hyps. 1, 4 & 6, the abstraction α, γ and α, γ is partially complete for Alg. 4 if and only if either α(L) contains an abstract value A such that γ(A) is an invariant for F , I, S or dually α(L) contains an abstract value A such that γ(A) is an invariant for F , I, S . Proof. The proof is similar to that of Th. 13 or its dual. 20 Patrick Cousot Then Def. 14 and Th. 15 are easily generalized in order to characterize the most abstract partially complete abstractions α, γ and α, γ for Alg.

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