Draft for review by W3C members and other interested parties. Publication as a working draft does not imply endorsement by the W3C membership. The RDF Model and Syntax Working Group will not allow early implementation to constrain their ability to make changes to this specification prior to final

,. The aim of this paper is t.o replace most of the (proven and unproven) group theory of IBS] by elementary com-binatorial argumenls. The rev & we prove is that relative to a random oracle f3, tbc meutioned matrix group prob-lems belong to (NPncoNP)L! Thr problems we consider arr membership in and order

groups of trajectories, (b) the capability to estimate the proportion of the population following each such trajectory group, (c) the capability to relate group membership probability to individual characteristics and circumstances, and (d) the capability to use the group membership probabilities

-time membership comparable sets have polynomial-size circuits. 3. For any function f and for any constant c ? 0, if a set is p f(n)-tt -reducible to a Pselective set, then the set is polynomial-time (1 + c) log f(n)-membership comparable. 4. For any C chosen from fPSPACE;UP;FewP;NP;C=P;PP;MOD 2 P; MOD 3 P

Abstract. Let I(f ) be a zero-dimensional ideal in C[z 1 , . . . , zn] defined by a mapping f . We compute the logarithmic residue of a polynomial g with respect to f . We adapt an idea introduced by Aizenberg to reduce the computation to a special case by means of a limiting process. We

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Introduction 3 2 Equational and Membership Constraints 5 3 Set Definitions 6 4 Normal Forms of C...

draft may be updated, replaced or rendered obsolete by other W3C documents at any time. It is inappropriate to use W3C Working Drafts as reference material or to cite them as other than "work in progress". This document is work in progress and does not imply endorsement by the W3C membership.

We show that for any concept class C the number of equiv-alence and membership queries that are needed to learn C is bounded from below by R(VC-dimension(C)). Fur-thermore we show that the required number of equivalence and membership queries is also bounded from below by R(LC- ARB(C) / log(1 + LC

to EXACT COVER BY 3-SETS, we exhibit the following problem to be NP-complete. Given the vector x 2 ! N with x(N ) = c(N ), decide whether there exists a coalition S such that x(S) ? c(S).