J. P. Grossmann, March 2002. Private communication.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is more dicult. We show that the checkerboard con guration can be reduced to dn=4e f1 if n 3 (mod 4)g stones, no matter who moves rst, and that this bound is best possible even if we do not have to alternate between white and black moves. This result was obtained independently by Grossman [2]. This paper is organized as follows. In Section 2, we analyze the reducibility of checkerboard con gurations on a line. In Section 3, we study reducibility of two dimensional rectangular checkerboard con gurations. And in Section 4 we show that deciding 1 reducibility is NP complete in general. ....

....Clobber (i.e. the board consists of a single row of stones) reducibility is more dicult. We show that the checkerboard who moves rst, and that this bound is best possible even if we do not have to alternate between white and black moves. This result was obtained independently by Grossman [2]. For n 1, the con guration An can be reduced to dn=4e f1 if n 3 (mod 4)g stones by an alternating sequence of moves, no matter who is to move rst. Proof. Split the con guration An into dn=4e substrings, all but possibly one of length four. Each substring of length one, two, or four can be ....

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J. P. Grossmann, March 2002. Private communication.

....1 reducibility. We show that the checkerboard configuration can be reduced to dn=4e f1 if n j 3 (mod 4)g stones, no matter who moves first, and that this bound is best possible even if we do not have to alternate between white and black moves. This result was obtained independently by Grossman [2]. This paper is organized as follows. In Section 2, we analyze the reducibility of onedimensional checkerboard configurations. In Section 3, we study reducibility of truly twodimensional rectangular checkerboard configurations. And in Section 4 we show that deciding 1 reducibility is NP complete ....

....one more stone in each pair of adjacent stones from the subblocks. Unfortunately, this is not possible, as shown by the following matching lower bound. The lower bound holds even if we are not forced to alternate between white and black moves. We give a simple proof for the theorem due to Grossman [2]. Theorem 2 Let n 1. Even if we are not restricted to alternating white and black moves, the configuration A n cannot be reduced to fewer than dn=4e f1 if n j 3 (mod 4)g stones. Proof: First, it is not possible to reduce A k to a single stone, for k = 3 or k 5. Second, each stone in the ....

J. P. Grossmann, March 2002. Private communication.

....the translation given here to allow program development from reactive speci cations as given by charts. Acknowledgements Our thanks to Mark Saaltink, who has suggested to us an ingenious, though necessarily complicated, schema iterator which does the job we mentioned at the end of section 2. 4 [12]. Thanks also the Peter Scholz for answering some of our basic questions about charts. Thanks nally to our colleagues on the ISuRF project [6] Lindsay Groves, Ray Nickson and Mark Utting, and to the Foundation for Research, Science and Technology (FRST) for grant UOW805 and to the University ....

M. Saaltink, March 2000. Private communication.

....; u 2 ; u 3 ; u 4 ) 7 (u 1 ; u 2 ; u 3 ; u 4 ) Lemma 6.3 The complexification E c of the curve E is a nonsingular connected elliptic curve. The composition fi ffi ff = extends to an automorphism c of E c which is fixed point free. Proof: The first statement of Lemma was proven in [G], GN] The biholomorphic extension c exists since E is Zariski dense in E c . The transformation : E E has no fixed points. It follows from the classification of automorphisms of elliptic curves that c is also fixed point free. 2 In particular the self map of E preserves the ....

M.L. Green, private communication.

....real spinor invariant. From this construction we derive the invariant tensors and the relations among them. Upon completion of this work, we received [19] which arrives at many of the same results in the G 2 theory. 2 This result has long been implicit in the literature; recent proofs of it are [16,17]. 2. General results in exceptional models In this section we will make some general observations on models based on exceptional groups, with matter quark fields Q i ff in the defining, or fundamental, representation. Here greek indices are group indices and latin indices label flavors. ....

....Although explicit parameterizations of these can be given for the non exceptional groups [21,4,5] the complicated algebraic structure of the exceptional groups makes them more challenging. Alternatives are to decompose the exceptional groups into non exceptional subgroups, or to use the fact [16,17] that flat directions can be parametrized by the gauge invariant polynomials in the quark fields. In this paper we adopt the latter approach. To form these polynomials we need the invariant tensors in the fundamental representation. The primitive tensors from which these can be constructed are ....

J. March-Russell, private communication.

....log maintenance has very low cost. For example, for the T2b traversal from the OO7 benchmark [8] the overhead for maintaining an undo log was less than 2.5 of non commit latency for a hot traversal that used no fetch requests, and less than 0. 5 for a traversal that did use fetch requests [13]. For the T2b traversal, roughly one in four object accesses is a write; we expect most workloads have low undo log costs compared to this traversal. Given the low overhead of undo log maintenance, we decided not to introduce a CPU charge for copy on write in our simulation model. To verify that ....

M. Castro, March 1996. Private Communication.

....tries to localize the cause of the illegal messages. TRW Corporation is involved in a United States Department of Defense research project to develop a network management expert system that ultimately will be capable of providing centralized network management activities for a nationwide network [24]. A prototype is currently being designed that will be able to monitor and control the activities of up to 40,000 network devices. A network device 16 can be an object such as a personal computer, printer, workstation, or a even a communications processor handling multiple interactive users. ....

Green, B., March 1991. Private Communication.

No context found.

J. P. Grossmann, March 2002. Private communication.

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T. Green, 2000, private communication.

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Green, S., private communication, Cleveland, OH, Dec.

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