Succinct: use new formalism in definitions

fs-succinct/succinct.tex

@@ -24,13 +24,13 @@ The information-theoretical optimum is $OPT(n) := \lceil\log |X(n)|\rceil$
 Now we can define three classes of data structures based on their fine-grained space
 efficiency:
 
-\defn{An {\I implicit data structure} is one that uses at most $OPT(n) + \O(1)$ bits of space.}
+\defn{An {\I implicit data structure} is one with $s(n) \le OPT(n) + \O(1)$.}
 
 A typical implicit data structure contains just its elements in some order and nothing more.
 Examples include sorted arrays and heaps.
 
-\defn{A {\I succinct data structure} is one that uses at most $OPT(n) + {\rm o}(OPT(n))$ bits of space.}
-\defn{A {\I compact data structure} is one that uses at most $\O(OPT(n))$ bits of space.}
+\defn{A {\I succinct data structure} is one with $s(n) \le OPT(n) + {\rm o}(OPT(n))$.}
+\defn{A {\I compact data structure} is one with $s(n) \le \O(OPT(n))$.}
 
 Note that some linear-space data structures are not even compact --  because we
 are counting bits now, not words. For example, a linked list representing a