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412 1418 V 148 w(Some)d(lik)o(e)f(it)i(hot,)g(some)f(lik)o(e)g(it)g(cold,)p 1316 1418 V 175 w(1100)j(1110)g(1010)g(0111)p 1805 1418 V 143 1479 V 266 1461 a(5)p 412 1479 V 148 w(Some)d(lik)o(e)f(it)i(in)g (the)g(p)q(ot,)p 1316 1479 V 410 w(1110)i(1111)g(1110)g(0011)p 1805 1479 V 143 1539 V 266 1521 a(6)p 412 1539 V 148 w(Nine)d(da)o(ys)h(old.)p 1316 1539 V 599 w(1010)i(1100)g(0100)g(1100)p 1805 1539 V 144 1541 1662 2 v 0 1795 a Fn(2.2)70 b(Searc)n(hing)22 b(on)i(Signatures)0 1888 y Fs(T)l(o)18 b(c)o(hec)o(k)d(whether)i(a)h (term)e Fm(T)23 b Fs(o)q(ccurs)18 b(in)f(a)h(do)q(cumen)o(t,)e(c)o(hec) o(k)f(whether)i(all)g(the)g(bits)g(whic)o(h)g(are)g(set)0 1948 y(in)g Fm(T)7 b Fs('s)16 b(signature)h(are)g(also)g(set)g(in)g (the)g(do)q(cumen)o(t's)e(descriptor.)23 b(If)16 b(not,)h Fm(T)24 b Fs(do)q(es)17 b(not)h(app)q(ear)g(in)e(the)0 2008 y(do)q(cumen)o(t.)33 b(If)20 b(so,)i Fm(T)27 b Fo(pr)n(ob)n(ably) 19 b Fs(o)q(ccurs)i(in)g(the)f(do)q(cumen)o(t;)h(b)q(ecause)f(some)g 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b(the)f(follo)o(wing)g(\(naiv)o(e\))g(pro)q (cedure:)34 b(to)23 b(\014nd)g(the)0 2489 y(descriptor)14 b(strings)h(for)g(whic)o(h)f(the)g(bits)g(in)g(a)h(giv)o(en)f (signature)h(are)f(set,)g(pull)g(out)h(all)f(descriptors,)g(and)0 2550 y(for)g(eac)o(h)f(descriptor,)g(c)o(hec)o(k)f(whether)h(the)h (appropriate)g(bits)g(are)f(set)h(for)g(eac)o(h)f(descriptor.)20 b(When)13 b(the)0 2610 y(descriptors)j(are)f(long)i(and)f(there)f(are)h (man)o(y)e(\014les,)h(this)h(approac)o(h)g(will)f(in)o(v)o(olv)o(e)e (man)o(y)h(disk)i(accesses,)0 2670 y(and)h(will)e(therefore)h(b)q(e)g (to)q(o)h(exp)q(ensiv)o(e.)938 2795 y(248)p eop %%Page: 249 4 249 3 bop 73 50 a Fs(A)11 b(substan)o(tially)f(more)g(e\016cien)o(t)f (metho)q(d)h(is)h(to)g(access)g(columns)e(of)j(the)e(signature)i (\014le,)e(rather)h(than)0 110 y(ro)o(ws.)25 b(This)17 b(tec)o(hnique)e(is)i(called)g Fo(bit-slicing)p Fs(.)26 b(The)17 b(signature)h(\014le)e(is)i(stored)f(on)h(disk)f(in)f(transp)q (osed)0 170 y(form.)k(That)c(is,)f(the)h(signature)g(\014le)f(is)g (stored)h(in)f(column-ma)s(jor)e(order;)j(in)f(the)h(naiv)o(e)e (approac)o(h,)i(the)0 230 y(signature)k(\014le)e(w)o(as)i(stored)f(in)g (ro)o(w-ma)s(jor)g(order.)30 b(T)l(o)20 b(pro)q(cess)g(a)f(query)g(for) g(a)h(single)f(term,)e(only)i Fm(b)0 291 y Fs(columns)e(need)h(to)g(b)q (e)h(read)f(from)g(disk;)g(in)g(the)g(naiv)o(e)f(approac)o(h,)i(the)g (en)o(tire)d(signature)j(\014le)f(needed)0 351 y(to)j(b)q(e)f(read.)33 b(The)20 b(bit)o(wise)f Fk(and)h Fs(of)g(these)g Fm(b)g Fs(columns)f(yields)g(the)h(do)q(cumen)o(ts)f(in)g(whic)o(h)h(the)g (term)0 411 y(probably)13 b(o)q(ccurs.)21 b(F)l(or)13 b(example,)e(to)i(c)o(hec)o(k)e(for)i(the)g(presence)f(of)h Fo(p)n(orridge)p Fs(,)f(tak)o(e)g(the)h Fk(and)f Fs(of)h(columns)0 471 y(t)o(w)o(o,)j(six,)f(and)i(elev)o(en,)d(to)i(obtain)h([110110])832 453 y Fl(T)861 471 y Fs(.)k(\(This)c(query)e(returned)h(t)o(w)o(o)g (false)g(matc)o(hes.\))0 613 y Fn(2.3)70 b(Query)22 b(logic)g(on)h (signature)g(\014les)0 705 y Fs(W)l(e)15 b(ha)o(v)o(e)g(seen)g(that)h (collisions)f(b)q(et)o(w)o(een)g(term)e(signatures)k(can)e(cause)h(a)g (w)o(ord)g(to)g(seem)d(presen)o(t)i(in)h(a)0 766 y(do)q(cumen)o(t)g (when)i(in)g(fact)g(the)f(w)o(ord)h(is)g(absen)o(t;)g(on)g(the)g(other) g(hand,)g(w)o(ords)h(that)f(seem)e(absen)o(t)i(are)0 826 y(absen)o(t.)k(If,)15 b(for)i(example,)d Fo(p)n(e)n(ase)i Fs(is)g(absen)o(t)h(from)e(a)i(do)q(cumen)o(t)e Fm(D)q Fs(,)i(then)f(the)g(answ)o(er)h(to)g(\\Is)f Fo(p)n(e)n(ase)g Fs(is)0 886 y Fm(D)q Fs(?")23 b(is)16 b(No;)g(if)f Fo(p)n(e)n(ase)h Fs(seems)f(to)i(b)q(e)f(presen)o(t,)f(then)h(the)g(answ)o(er)h(is)f(Ma) o(yb)q(e.)73 946 y(F)l(or)i(queries)e(with)i(negated)g(terms)e(\(for)i (example,)d(\\Is)j Fo(p)n(e)n(ase)f Fs(absen)o(t)h(from)e(do)q(cumen)o (t)h Fm(d)p Fs(?"\))26 b(the)0 1006 y(situation)c(is)g(rev)o(ersed.)38 b(F)l(or)22 b(example,)f(since)g Fo(p)n(e)n(ase)h Fs(has)g(bits)g(six,) h(eigh)o(t,)f(and)h(16)g(set,)g(it)e(cannot)0 1067 y(o)q(ccur)14 b(in)g(do)q(cumen)o(ts)f(three,)g(four,)i(or)f(six,)g(so)g(for)h(these) e(do)q(cumen)o(ts)g(the)h(appropriate)h(answ)o(er)f(is)g(Y)l(es.)0 1127 y(Ho)o(w)o(ev)o(er,)g(the)i(other)g(do)q(cumen)o(ts)f(migh)o(t)g (con)o(tain)h Fo(p)n(e)n(ase)p Fs(,)f(so)i(for)f(these)g(do)q(cumen)o (ts)f(the)h(appropriate)0 1187 y(answ)o(er)g(is)h(Ma)o(yb)q(e.)73 1247 y(More)24 b(generally)l(,)h(queries)f(in)g(signature)g(\014les)g (need)g(to)h(b)q(e)g(ev)m(aluated)f(in)g(three-v)m(alued)g(logic.)0 1307 y(A)o(tomic)13 b(queries)h(\(e.g.)20 b(\\Is)15 b Fo(nine)i Fs(presen)o(t?"\))k(ha)o(v)o(e)14 b(t)o(w)o(o)h(resp)q (onses,)h(No)f(and)h(Ma)o(yb)q(e.)k(More)15 b(complex)0 1368 y(queries)f(|)h(queries)f(built)g(from)g(atomic)f(queries)h(using) h Fk(not)p Fs(,)g Fk(and)o Fs(,)g(and)g Fk(or)g Fs(|)g(get)g(ev)m (aluated)g(using)0 1428 y(the)h(follo)o(wing)g(rules:)p 446 1476 212 2 v 445 1536 2 61 v 467 1518 a Fk(not)p 578 1536 V 657 1536 V 446 1538 212 2 v 445 1598 2 61 v 497 1580 a(n)p 578 1598 V 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1889 a(Do)q(c.)p 432 1907 V 59 w(s)p 519 1907 V 64 w(h)p 606 1907 V 60 w(p)p 693 1907 V 55 w Fk(not)g Fs(h)p 878 1907 V 50 w(s)g Fk(or)g(not)g Fs(h)p 1176 1907 V 50 w(\(s)g Fk(or)g(not)g Fs(h\))h Fk(and)e Fs(p)p 1664 1907 V 285 1909 1381 2 v 284 1969 2 61 v 347 1951 a(1)p 432 1969 V 87 w Fk(m)p 519 1969 V 50 w(m)p 606 1969 V 50 w(m)p 693 1969 V 99 w(m)p 878 1969 V 204 w(m)p 1176 1969 V 356 w(m)p 1664 1969 V 284 2029 V 347 2011 a Fs(2)p 432 2029 V 87 w Fk(m)p 519 2029 V 50 w(m)p 606 2029 V 50 w(m)p 693 2029 V 99 w(m)p 878 2029 V 204 w(m)p 1176 2029 V 356 w(m)p 1664 2029 V 284 2090 V 347 2072 a Fs(3)p 432 2090 V 90 w Fk(n)p 519 2090 V 56 w(n)p 606 2090 V 56 w(n)p 693 2090 V 105 w(y)p 878 2090 V 211 w(y)p 1176 2090 V 362 w(n)p 1664 2090 V 284 2150 V 347 2132 a Fs(4)p 432 2150 V 87 w Fk(m)p 519 2150 V 50 w(m)p 606 2150 V 53 w(n)p 693 2150 V 102 w(m)p 878 2150 V 204 w(m)p 1176 2150 V 360 w(n)p 1664 2150 V 284 2210 V 347 2192 a Fs(5)p 432 2210 V 87 w Fk(m)p 519 2210 V 50 w(m)p 606 2210 V 50 w(m)p 693 2210 V 99 w(m)p 878 2210 V 204 w(m)p 1176 2210 V 356 w(m)p 1664 2210 V 284 2270 V 347 2252 a Fs(6)p 432 2270 V 90 w Fk(n)p 519 2270 V 56 w(n)p 606 2270 V 56 w(n)p 693 2270 V 105 w(y)p 878 2270 V 211 w(y)p 1176 2270 V 362 w(n)p 1664 2270 V 285 2272 1381 2 v 0 2385 a Fn(2.4)70 b(Cho)r(osing)23 b(signature)g(width)0 2477 y Fs(Ho)o(w)15 b(should)h Fm(W)22 b Fs(b)q(e)15 b(c)o(hosen)g(so)h(that)g(the)f(exp)q(ected)f(n)o(um)o(b)q(er)g(of)h (false)g(matc)o(hes)f(is)h(less)g(than)h(or)g(equal)0 2537 y(to)h(some)e(n)o(um)o(b)q(er)f Fm(z)r Fs(?)22 b(It)16 b(turns)g(out)h(that)g Fm(W)23 b Fs(should)17 b(b)q(e)f(set)g(to)921 2606 y(1)p 784 2628 299 2 v 784 2674 a(1)c Fr(\000)e Fs(\(1)i Fr(\000)f Fm(p)p Fs(\))1017 2660 y Fj(1)p Fl(=B)1888 2640 y Fs(\(9\))938 2795 y(249)p eop %%Page: 250 5 250 4 bop 0 50 a Fs(where)122 142 y Fm(p)p Fs(,)17 b(the)g(probabilit)o (y)f(that)i(an)g(arbitrary)f(bit)f(in)h(a)h(do)q(cumen)o(t)e (descriptor)g(is)h(set,)g(is)g(giv)o(en)122 203 y(b)o(y)202 183 y Fl(z)p 195 191 32 2 v 195 220 a(N)231 182 y Fj(1)p Fl(=b)284 203 y Fs(;)122 282 y Fm(B)s Fs(,)d(the)h(total)h(n)o(um)o(b)q (er)d(of)i(bits)g(set)g(in)g(the)g(signature)g(of)g(an)h(a)o(v)o(erage) f(do)q(cumen)o(t,)e(is)i(giv)o(en)122 342 y(b)o(y)200 321 y Fl(f)p 195 331 V 195 360 a(N)242 342 y Fr(\001)273 323 y Fl(b)p 272 331 17 2 v 272 360 a(q)294 342 y Fs(;)122 422 y Fm(N)21 b Fs(is)c(the)f(n)o(um)o(b)q(er)e(of)j(do)q(cumen)o(ts;) 122 482 y Fm(f)22 b Fs(is)16 b(the)g(n)o(um)o(b)q(er)e(of)j(\()p Fo(do)n(cument,)h(term)p Fs(\))e(pairs;)122 542 y Fm(b)g Fs(is)g(the)g(n)o(um)o(b)q(er)e(of)j(bits)f(p)q(er)g(query;)g(and)122 602 y Fm(q)i Fs(is)e(the)g(n)o(um)o(b)q(er)e(of)j(terms)d(in)i(eac)o(h) g(query)l(.)0 695 y(The)i(analysis)f(used)h(to)g(deriv)o(e)e(\(9\))i (can)g(b)q(e)g(found)g(in)f(Witten,)g(Mo\013at,)i(and)f(Bell,)e Fo(Managing)k(Giga-)0 755 y(bytes)p Fs(,)g(c)o(hapter)e(3,)h(Section)f (3.5.)30 b(One)18 b(assumption)g(made)g(in)h(this)f(analysis)h(is)g 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