The index has provably small space footprints, is orders of magnitude smaller and faster to create/incrementally maintain than exact solutions, and the algorithms provide approximate answers, with an error that is controlled by a user-specified parameter.
The advantages over ad hoc heuristic methods are threefold: (i) having provably optimal solutions at hand allows evaluating the quality of a model, e.g. the appropriateness of an objective function.
The documents had provably crossed Hiss's desk at the State Department and been copied on Hiss's typewriter, by his wife, Priscilla.
The energy of dis-integrity in our country, which has actually been with us provably from the beginning but has likely increased over time, is pervasive.
LOS ANGELES — Of all the clichés about this town that are provably untrue — no one reads, or has the lips that God gave them — it is undeniable that Los Angeles has often been a poor guardian of its physical history.
This is the case if, for example, the provability predicate ProvF x) has been chosen as a Σ01-formula: The Gödel sentence is then provably equivalent to the universal formula ∀x¬PrfF x, ⌈GF⌉).
The idea of we've never been able to provably own unique digital assets is crazy to me," Dinch notes.
Recently, much attention has been focused on designing provably secure cryptographic scheme in the presence of key leakage, and many constructions are proposed by cryptography researchers.
Surprisingly, however, there has been little work towards designing provably efficient fully-distributed algorithms for computing PageRank.
Perhaps because of ingrained cultural beliefs about the infallibility of computation, people show a level of trust in computed outputs that is completely at odds with the reality that nearly zero provably error-free computer programs have ever been written.
This represents the first provably exact deterministic model of epidemic dynamics on finite heterogeneous systems which has been numerically evaluated.
