We explain how iteration over these structures can be handled using a restricted form of aliasing called local borrowing. To avoid introducing a memory model and to stay in the first-order logic background of SPARK, the relation between the iterator and the underlying structure is encoded as a...
From this starting point, the obvious way to evaluate recursive definitions is to begin with all the defined relations empty, and the iteratively compute new values for the relations, using the old relation values as input, until the relations produced as output are the same as the ones that ...
where Kn denotes the set of children of node n, rnk denotes the dependency relation between node n and its child node k, and hk is the hidden vector of the child node k. The tree structures used for RNNs include constituency tree and dependency tree. In a constituency tree, the words ...
A relation R on the natural numbers is recursive iff it is representable in some consistent finitely axiomatizable theory (in a language with 0 and S). Church's thesis now can be put more succinctly: A relation is decidable iff it is recursive. Or perhaps more accurately: The concept of...
2 Virtual Cache Lines - A Cache-Aware Data Structure This section presents the concepts behind the Virtual Cache Lines model. First, it discusses the relation between the configuration of the physical cache lines (currently only the L1 cache) on a given system and the virtual cache lines ...
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We impose that data sequences (wn) and (w′nwn′) verify (4), (6), (8) and (11), because they are intrinsic to recursions (a technical reason justifies (10)). In effect, (4) and (6) are obtained taking into account (2) in the inequalities |wn+1|≤|f(zn)−f(zn+1)|...
The sub-type relation for types of values coincides exactly with sublanguage concept of the set of sentences for all values of the given types. The latter point is one of the main reasons why vallang is called a language. The result of anyValue.toString() is a member of a precisely def...
But for the nested recurrence relation T212 we see that this is no longer true; there can be an unboundedly large lookback. OK, but let’s look back at the actual T212 sequence. Here it is up to larger values ofn: Or, plotting each point as a dot: ...
Recurrence relation can be used to analyze the time complexity of divide-and-conquer algorithms. Consider a problem of size n that can be broken into a smaller subproblems, where each is the size of nb, assuming n is a multiple of b, and suppose f(n) is a nondecreasing function, where...