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1 TRC vs DRC 2003. 10. 12 한욱신

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2 Queries in TRC and DRC TRC Q = {t| f(t)} where t is a (free) tuple variable and f(t) is a well-formed formula DRC Q = {x 1,x 2,..,x k | f(x 1,x 2,..,x k )} where x i is a (free) domain variable and f(x 1,x 2,..,x k ) is a well- formed formula

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3 Well-formed formula Wffs are constructed using the following rules Each atomic formula is a wff If P, Q are wffs, then so are NOT P, (P AND Q), (P OR Q), and (P Q) If x is a (tuple or domain) variable and P is a wff, then so are x P, and x P

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4 Atomic formulas in TRC and DRC TRC R(t) where R is a relation name and t is a tuple variable t i [A] t j [B] where t i and t j are tuple variables; A and B are attributes names; is a comparison operator (=,, , , ) t i [A] constant DRC R(x 1,x 2,…,x k ) where R is a relation name and x i is a domain variable or constant x y where x and y are domain variables x constant where x is a domain variable

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5 Example Schema Sailors(sid, sname, rating, age) Boats(bid, bname, color) Reserves(sid, bid, date)

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6 Q1) Find sailors who’ve reserved at least one boat sid (Sailors Reserves) {p|( r)( s)(Reserves(r) AND Sailors(s) AND /* initiate tuple variables */ r[sid] = s[sid] AND /* join condition */ p[1st attr] = s[sid])}/* projection */ {s| ( b)( d)( s2)( sn)( r)( a)(Reserves(s,b,d) AND Sailors(s2, sn, r,a) AND /* initiate tuple variables */ s = s2) /* join condition */ } Relational Algebra TRC DRC

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7 Q2) Find sid’s of sailors who’ve reserved a red or a green boat {p|( r)( s)( b)(Reserves(r) AND Sailors(s) AND Boats(b) AND /* initiate tuple variables */ r[sid] = s[sid] AND /* join condition */ r[bid] = b[bid] AND /* join condition */ (b[color] = ‘red’ OR b[color] = ‘green’) AND /* selection condition */ p[1st attr] = s[sname])}/* projection */ {s| ( b)( d)( s2)( sn)( r)( a)( b2)( bn)( c)(Reserves(s,b,d) AND Sailors(s2, sn, r,a) AND Boats(b2, bn, c) AND /* initiate tuple variables */ s = s2 AND b=b2 AND /* join condition */ (c = ‘red’ OR c = ‘green’))} Relational Algebra TRC DRC

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8 Q3) Find sid’s of sailors who’ve reserved a red and a green boat {p|( r)( s)( b)(Sailors(s) AND Boats(b1) AND Reserves(r1) AND Boats(b2) AND Reserves(r2) AND /* initiate tuple variables */ s[sid]=r1[sid] AND r1[bid]=b1[bid] AND s[sid]=r2[sid] AND r2[bid]=b2[bid] AND (b1[color]=‘red’ AND b2[color]=‘green’ AND p[1st attr] = s[sname])}/* projection */ {s| ( b)( d)( s2)( sn)( r)( a)( b2)( bn)( c) )( s2’)( sn’)( r’)( a’)( b2’)( bn’)( c’) ( Reserves(s,b,d) AND Sailors(s2, sn, r,a) AND Boats(b2, bn, c) AND Sailors(s2’, sn’, r’,a’) AND Boats(b2’, bn’, c’) AND /* initiate tuple variables */ s = s2 AND b=b2 AND s = s2’ AND b=b2’ AND/* join condition */ (c = ‘red’ AND c’ = ‘green’))} Relational Algebra TRC DRC

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Relational Algebra Content based on Chapter 4 Database Management Systems, (Third Edition), by Raghu Ramakrishnan and Johannes Gehrke. McGraw Hill, 2003.

Relational Algebra Content based on Chapter 4 Database Management Systems, (Third Edition), by Raghu Ramakrishnan and Johannes Gehrke. McGraw Hill, 2003.

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