All cryptographic hash functions that are now widely used are not based on hard mathematical problems.Those few functions that are constructed on hard mathematical problems are called provably secure.Finding collisions is then known to be as hard as solving the hard mathematical problem.…

When we saw her the whole story was reiterated with but few changes, which, however, from the standpoint of testimony were most important.We soon found we could get direct testimony on physical features which were provably untrue.For instance, the description of a certain hallway in a building where she had gone with one of the men interested in the events was totally unlike anything that existed there.…Cited from Pathology of Lying, Etc. by William and Mary Healy

A later Finnish report showed that only one victim had provably been shot at close range.The report from the Finnish team, however, was kept confidential by the EU until long after the war, and the team leader, Helena Ranta, issued a press release at the time containing her "personal opinion" and indicating differing and opposite findings.…

Many of these legends trace back to tall tales that Longley himself told while imprisoned in Giddings in 1877.Some of these stories are provably false, while others could be true but lack any contemporary corroborating evidence.Longley's lies appear to have been motivated partly by his desire to rival John Wesley Hardin's reputation as a killer.…

Provably secure means that finding collisions is as difficult as some known hard mathematical problem.Unlike other secure collision-resistant hashes, VSH is efficient and usable in practice.…

It means that if one could find collisions, one would be able to solve the underlying mathematical problem which is assumed to be hard and unsolvable in polynomial time.Functions with these properties are known provably secure and are quite unique among the rest of hash functions.Nevertheless second pre-image (and thus a collision) was later found because the assumptions given in the proof were too strong.…

Announcing a product that does not exist to gain a competitive advantage is illegal via Section 2 of the Sherman Antitrust Act of 1890, but few hardware or software developers have been found guilty of it.The section requires proof that the announcement is both provably false, and has actual or likely market impact.False or misleading announcements designed to influence stock prices are illegal under United States securities fraud laws.…

The design of the latest version of FSB has however taken this attack into account and remains secure to all currently known attacks.As usual, provably security comes at a cost.FSB is slower than traditional hash functions and uses quite a lot of memory, which makes it impractical on memory constrained environments.…

Jones died on March 3, 1884 after a prolonged illness in Wailuku, Maui Hawaiian newspapers published a number of obituaries using information Jones had provided over the years to detail his life before his arrival in the islands.Roughly half of the facts provided by Jones are provably false with another quarter being unverifiable.…

The idea is to choose \lambda as small as possible so that all elements are provably covered with non-zero probability.

Global value numbering works by assigning a value number to variables and expressions.To those variables and expressions which are provably equivalent, the same value number is assigned.…

There exists a computable enumeration of the halting set, but not one that lists the elements in an increasing ordering.If there were one, then the halting set would be decidable, which is provably false.In general, being recursively enumerable is a weaker condition than being a decidable set.…

Lipton showed that randomized testing can be provably useful, given the problem satisfied certain properties.Proving correctness of a program is one of the most important problems presented in computer science.…

A cryptographic hash function has provable security against collision attacks if finding collisions is provably polynomial-time reducible from problem P which is supposed to be unsolvable in polynomial time.The function is then called provably secure, or just provable.It means that if finding collisions would be feasible in polynomial time by algorithm A, we could find and use polynomial time algorithm R (reduction algorithm) that would use algorithm A to solve problem P, which is widely supposed to be unsolvable in polynomial time.…

Henry's son Otto the Great provably stayed at the Pfalz five times.

These forms of negation are logical negations, i.e. they state that something is provably not the case.Negation as failure states that a state of affairs cannot be proved, i.e. there is no information whether the state of affairs is the case or not.…

One such approximation is AIXItl, which performs as least as well as the provably best time t and space l limited agent.

Scruffies are hackers, who will cobble together a system built of anything - even logic.Neats care whether their reasoning is both provably sound and complete and that their machine learning systems can be shown to converge in a known length of time.Scruffies would like their learning to converge too, but they are happier if empirical experience shows their systems working than to have mere equations and proofs showing that they ought to.…

This guarantee is not given by most other provably secure hash functions.Known working attacks are: Generalized Birthday Attack, which takes 2 106 operations and inversion attacks which takes 2 448 operations for a standard parameter choice.…

In particular, files of random data cannot be consistently compressed by any conceivable lossless data compression algorithm: indeed, this result is used to define the concept of randomness in algorithmic complexity theory.It's provably impossible to create an algorithm that can losslessly compress any data.…