\relax 
\citation{[icalp]}
\citation{[Mil]}
\citation{[Bar]}
\citation{[le80]}
\citation{[le80]}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
\citation{[Win89]}
\citation{[levy]}
\citation{[le80]}
\citation{[Lam]}
\citation{[Kath]}
\citation{[KKSdV]}
\citation{[Mar]}
\citation{[adeq]}
\citation{[adeq]}
\citation{[rndrs]}
\citation{[rndrs]}
\citation{[levy]}
\citation{[le80]}
\citation{[K.S.]}
\citation{[Mar]}
\citation{[AL]}
\citation{[Oos]}
\citation{[Bar]}
\citation{[levy]}
\citation{[le80]}
\citation{[rndrs]}
\citation{[dndrs]}
\citation{[dndrs]}
\citation{[Win89]}
\citation{[dpes]}
\citation{[mfcs-tcs]}
\citation{[mfcs98]}
\citation{[icalp]}
\citation{[rndrs]}
\citation{[dndrs]}
\citation{[ldrs]}
\citation{[atoe-tcs]}
\citation{[atoe-tcs]}
\citation{[levy]}
\citation{[Kl.TRS]}
\citation{[Hin]}
\citation{[Kl.TRS]}
\citation{[levy]}
\citation{[B.L.]}
\citation{[H.L.]}
\citation{[le80]}
\citation{[Sta]}
\citation{[GLM]}
\citation{[GLM]}
\citation{[Oos.th]}
\citation{[Mel]}
\citation{[Raa.th]}
\citation{[GLM]}
\citation{[adeq]}
\citation{[Laf]}
\citation{[GAL.LL]}
\citation{[GirUL]}
\@writefile{toc}{\contentsline {section}{\numberline {2}Deterministic Residual and Family Structures}{4}}
\citation{[GLM]}
\citation{[Sta]}
\citation{[H.L.]}
\citation{[le80]}
\citation{[Sta]}
\newlabel{D.levy.str.}{{2.3}{5}}
\citation{[rndrs]}
\citation{[ldrs]}
\newlabel{D.ext.reductions.}{{2.5}{6}}
\citation{[rndrs]}
\citation{[atoe-tcs]}
\citation{[levy]}
\citation{[le80]}
\citation{[K.S.]}
\citation{[Mar]}
\citation{[AL]}
\citation{[Oos]}
\citation{[rndrs]}
\citation{[le80]}
\newlabel{L.disj.red.creat.}{{2.6}{7}}
\newlabel{L.ext.lem.mult.}{{2.7}{7}}
\newlabel{D.DRS.}{{2.8}{7}}
\citation{[atoe-tcs]}
\citation{[acoi]}
\citation{[ldrs]}
\citation{[acoi]}
\citation{[atoe-tcs]}
\newlabel{D.lin.dfs.drs.}{{2.10}{8}}
\newlabel{P.on.ca.for.}{{2.11}{8}}
\citation{[Bar]}
\citation{[H.L.]}
\citation{[Kl.CRS]}
\citation{[dndrs]}
\newlabel{T.lin.dr.sta.df.}{{2.12}{9}}
\newlabel{L.res.fam.fam.}{{2.13}{9}}
\newlabel{T.line.zig.}{{2.14}{9}}
\newlabel{R.mult.}{{2.15}{9}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Decomposition of Reductions in ASDRSs}{9}}
\newlabel{S.res.proj.}{{3}{9}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Relative Standardization}{9}}
\newlabel{SS.stan.}{{3.1}{9}}
\newlabel{D.red.need.ess.}{{3.1}{9}}
\citation{[dndrs]}
\newlabel{D.ess.rel.red.}{{3.2}{10}}
\newlabel{L.need.monot.}{{3.3}{10}}
\newlabel{L.era.and.ess.im.ne.}{{3.4}{10}}
\newlabel{L.dif.re.sa.his.}{{3.5}{10}}
\newlabel{L.un.re.un.}{{3.6}{10}}
\citation{[ldrs]}
\citation{[K-tra]}
\citation{[Ken96]}
\newlabel{L.un.cr.un.}{{3.7}{11}}
\newlabel{T.can.self-need.var.}{{3.8}{11}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Characterizing relative standardization using families}{12}}
\newlabel{L.sta.eq.sa.fam.}{{3.10}{12}}
\newlabel{L.sfa.is,fam.of.se.}{{3.11}{12}}
\newlabel{L.leq.sfam.}{{3.12}{13}}
\newlabel{P.leqv.sam.se.es.fa.}{{3.13}{13}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}The Projection Concept}{13}}
\newlabel{D.proj.}{{3.14}{13}}
\newlabel{L.stan.est.}{{3.15}{14}}
\newlabel{E.proj.}{{3.16}{14}}
\newlabel{C.proj.char.fam.}{{3.17}{14}}
\newlabel{L.err.st.both.le.cla.}{{3.18}{14}}
\newlabel{C.proj.inv.}{{3.19}{14}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}The Restriction Concept}{15}}
\newlabel{D.resp.restr.}{{3.21}{15}}
\newlabel{L.corr.rest.}{{3.22}{15}}
\newlabel{L.char.resp.}{{3.24}{16}}
\newlabel{L.resp.invar.le.eq.}{{3.25}{16}}
\newlabel{L.ind.union.subt.}{{3.26}{16}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.5}The Decomposition Theorem}{17}}
\newlabel{L.inv.proj.}{{3.27}{17}}
\newlabel{L.sum.rstr.eq.se.of.sum.}{{3.28}{17}}
\newlabel{T.dec.thm.}{{3.30}{17}}
\newlabel{D.resp.restr.mult.}{{3.31}{17}}
\newlabel{C.dec.thm.}{{3.32}{18}}
\@writefile{toc}{\contentsline {section}{\numberline {4}The Geometry of Conflict-free Reduction Spaces}{18}}
\newlabel{S.geom.}{{4}{18}}
\citation{[colog]}
\citation{[rta]}
\citation{[Mar]}
\newlabel{L.rel.cof.}{{4.3}{19}}
\newlabel{L.rest.v.proj.}{{4.4}{19}}
\newlabel{D.basis.}{{4.5}{19}}
\citation{[le80]}
\newlabel{E.bas.}{{4.6}{20}}
\newlabel{L.ind.resp.red.}{{4.7}{20}}
\citation{[rndrs]}
\citation{[atoe-tcs]}
\citation{[ctrs]}
\newlabel{P.ind.union.subt.}{{4.8}{21}}
\newlabel{T.ind.dec.thm.}{{4.9}{21}}
\newlabel{C.ind.dec.thm.}{{4.10}{21}}
\@writefile{toc}{\contentsline {section}{\numberline {5}The Optimal Decomposition Theorem}{21}}
\newlabel{S.rel.geom.}{{5}{21}}
\citation{[rndrs]}
\citation{[atoe-tcs]}
\citation{[mfcs-tcs]}
\citation{[mfcs98]}
\citation{[mfcs98]}
\newlabel{D.rel.need.}{{5.1}{22}}
\newlabel{T.aff.opt.}{{5.2}{22}}
\newlabel{D.rel.ord.}{{5.3}{22}}
\citation{[rndrs]}
\citation{[rndrs]}
\newlabel{D.rel.basis.}{{5.5}{23}}
\newlabel{L.prop.rel.need.}{{5.6}{23}}
\newlabel{L.ind.nee.}{{5.7}{24}}
\newlabel{D.f.m.compl.}{{5.8}{24}}
\newlabel{L.ref.opt.decomp.}{{5.9}{24}}
\newlabel{L.s.f.compl.res.sfcomp.ag.}{{5.10}{25}}
\newlabel{T.opt.fmcompl.}{{5.11}{25}}
\citation{[acoi]}
\citation{[atoe-tcs]}
\citation{[H.L.]}
\citation{[rta]}
\citation{[caap]}
\citation{[C.Chap.]}
\citation{[C.Chap.]}
\citation{[caap]}
\citation{[csl98]}
\citation{[Levy76]}
\newlabel{T.opt.decomp.}{{5.12}{26}}
\newlabel{C.opt.decomp.}{{5.13}{26}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Conclusions}{26}}
\newlabel{S.concl.}{{6}{26}}
\citation{[Kl.TRS]}
\citation{[Rus]}
\bibcite{[AL]}{AL94}
\bibcite{[Bar]}{Bar84}
\bibcite{[B.L.]}{BeL\'e79}
\bibcite{[C.Chap.]}{Cou90}
\bibcite{[GirUL]}{Gir91}
\bibcite{[ctrs]}{GK94}
\bibcite{[rndrs]}{GK96}
\bibcite{[GLM]}{GLM92}
\bibcite{[GAL.LL]}{GAL92}
\bibcite{[H.L.]}{HL91}
\bibcite{[Hin]}{Hin64}
\bibcite{[Kath]}{Kat90}
\bibcite{[Ken96]}{Ken96}
\bibcite{[K.S.]}{KS89}
\bibcite{[KKSdV]}{KKSV93}
\bibcite{[adeq]}{KKSV94}
\bibcite{[K-tra]}{KKSV95}
\bibcite{[colog]}{Kha88}
\bibcite{[rta]}{Kha93}
\bibcite{[caap]}{Kha94}
\bibcite{[mfcs98]}{Kha98}
\bibcite{[dndrs]}{KG96}
\bibcite{[dndrs-rep]}{KG96a}
\bibcite{[ldrs]}{KG97}
\bibcite{[icalp]}{KG97a}
\bibcite{[dpes]}{KG97b}
\bibcite{[acoi]}{KG97c}
\bibcite{[atoe-tcs]}{KG98}
\bibcite{[mfcs-tcs]}{KG98a}
\bibcite{[csl98]}{KP98}
\bibcite{[Kl.CRS]}{Klo80}
\bibcite{[Kl.TRS]}{Klo92}
\bibcite{[Laf]}{Laf90}
\bibcite{[Lam]}{Lam90}
\bibcite{[Levy76]}{L\'ev76}
\bibcite{[levy]}{L\'ev78}
\bibcite{[le80]}{L\'ev80}
\bibcite{[Mar]}{Mar92}
\bibcite{[Mil]}{Mil92}
\bibcite{[Mel]}{Mel96}
\bibcite{[Oos.th]}{Oos94}
\bibcite{[Oos]}{Oos96}
\bibcite{[Raa.th]}{Raa96}
\bibcite{[Rus]}{Rus87}
\bibcite{[Sta]}{Sta89}
\bibcite{[Win89]}{Win89}