add authors comment

add main file

main.typ

@@ -87,9 +87,10 @@ Simplified version (to get the idea)
 for each tuple tr in r: (for each tuple ts in s: test pair (tr, ts))
 ```
 
-// TODO: Add seek information
 Block transfer cost: $n_r dot b_s + b_r$ block transfers would be required,
-where $b_r$ -- blocks in relation $r$, same for $s$.
+where $b_r$ -- blocks in relation $r$, same for $s$. Each scan of the inner
+relation requires one seek, and the scan of the outer relation requires one seek
+per block, leading to a total of $2 dot b_r$ seeks.
 
 == Block-nested join
 
@@ -275,7 +276,8 @@ The concept of conflict equivalence leads to the concept of conflict
 serializability. We say that a schedule $S$ is *conflict serializable* if it is
 conflict equivalent to a serial schedule.
 
-=== Serializability graph
+// TODO: rename to precedence
+=== Precedence graph
 
 Simple and efficient method for determining the conflict seriazability of a
 schedule. Consider a schedule $S$. We construct a directed graph, called a
@@ -310,6 +312,15 @@ locking protocol. We say that a locking protocol ensures conflict
 serializability if and only if all legal schedules are *conflict serializable*;
 in other words, for all legal schedules the associated $->$ relation is acyclic.
 
+*Recoverable* schedule is one where, for each pair of transactions $T_i$ and
+$T_j$ such that $T_j$ reads a data item previously written by $T_i$, the commit
+operation of $T_i$ appears before the commit operation of $T_j$.
+
+*Cascadeless* schedule is one where, for each pair of transactions $T_i$ and
+$T_j$ such that $T_j$ reads a data item previously written by $T_i$, the commit
+operation of $T_i$ appears before the read operation of $T_j$. Every cascadeless
+schedule is also recoverable.
+
 === Lock-based
 
 *Shared Lock* -- If a transaction $T_i$ has obtained a shared-mode lock (denoted
@@ -475,7 +486,8 @@ $B=5;T_"disk"=0.001;T_"seek"=0.1$
 === Nested-Loop Join Method
 + Nested-loop join:
   - For each pattern in $r_1$, search all patterns in $r_2$.
-+ Total Combinations: $75435 dot 11456=$
++ Total Combinations: $75435 dot 11456$
 + Time Calculation for Nested-Loop Join:
   - Reading and searching time for each combination: $0.001+0.1=0.101 "ms"$
-  - Total time: $75435 dot 11456 dot 0.101 = 87282519.36 "ms"$
+  - Total time: $75435 dot 11456 dot 0.101 = 87282519.36 "ms"$ [Authors comment:
+    seems fishy]