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 hotel and convention membership, Lake LBJ, Texas, July 26– 29, 2000, simply sooner than the AAAI 2000 convention in Austin. past SARA meetings came about 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 considering that 1989. This year’s symposium was once really scheduled to occur at Lago Vista golf equipment & hotel on Lake Travis yet, a result of resort’s failure to pay taxes, the convention needed to be moved overdue 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 can be the ?rst SARA for which the lawsuits were released within the LNAI sequence of Springer-Verlag. we are hoping that it is a re?ection of the elevated adulthood of the ?eld and that the elevated visibility introduced through the book of this quantity might help the self-discipline develop even extra. Abstractions, reformulations, and approximations (AR&A) have came across - plications in various disciplines and difficulties together with automated progr- ming, constraint pride, layout, analysis, computer 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**

The diﬀerence 7 − 4 = 3 accounts for the diﬀerence between the left-side value functions. We would like to exploit this regularity to represent the left-side value function only once. The MAXQ value function decomposition is a way of achieving this. The idea is to decompose the Q(p, s, a) value into the sum of two components. The ﬁrst component is the expected total reward received while executing action a, and the second component is the expected total reward of completing parent task p after a has returned.

D. Dams, O. Grumberg, and R. Gerth. Abstract interpretation of reactive systems. ACM Transactions on Programming Languages and Systems, 19(2):253–291, 1997. S. L. Dill, and S. Park. Experience with predicate abstraction. In N. Halbwachs and D. Peled, editors, Proceedings of the Eleventh International Conference on Computer Aided Verification, CAV ’99, Trento, Italy, Lecture Notes in Computer Science 1633, pages 160–171. Springer-Verlag, Berlin, Germany, 6–10 July 1999. W. Floyd. Assigning meaning to programs.

The respective values of X and Y after n ≥ 0 iterations, if ever, are X n and Y n as respectively deﬁned in the proofs of Th. 10 and Th. 20. If the algorithm does terminate, then 1. either the loop is never entered so the values of X and Y are respectively X 0 = α(I) and Y 0 = α(S) such that γ(X) ≤ S | I ≤ γ(Y ), in which case Alg. 7 correctly returns I don’t know ; or the loop is entered at least once so that upon exit after n ≥ 1 iterations, we have X n = α(I ∨F ◦ γ(X n ))|Y n = α(S ∧ F ◦ γ(Y n ))|γ(X n ) ≤ S |I ≤ γ(Y n ).