* Soundness: if the statement is false, no prover, even if it doesn't follow the protocol, can convince the honest verifier that it is true, except with some small probability.

# Soundness: if the statement is false, no cheating prover can convince the honest verifier that it is true, except with some small probability.

Soundness is among the most fundamental properties of mathematical logic.

Soundness properties come in two main varieties: weak and strong soundness, of which the former is a restricted form of the latter.

Soundness of a deductive system is the property that any sentence that is provable in that deductive system is also true on all interpretations or structures of the semantic theory for the language upon which that theory is based.

* ( Soundness ) Every provable second-order sentence is universally valid, i. e., true in all domains under standard semantics.

* Soundness, a logical term meaning that an argument is valid and its premises are true

Soundness guarantees that all possible behaviours are preserved while completeness guarantees that no behaviour is added by the encoding.

* October 1992 – The Housing and Community Development Act of 1992 codifies within its language the Federal Housing Enterprises Financial Safety and Soundness Act of 1992 that creates the Office of Federal Housing Enterprise Oversight, and mandates HUD to set goals for lower income and underserved housing areas for the GSEs Fannie Mae and Freddie Mac

* Soundness: If x ∉ L then for every π, V < sup > π </ sup >( x ) accepts with probability at most s ( n ).

Validity and Soundness in the Internet Encyclopedia of Philosophy.

In Quality of Management they scored second place, third in Long Term Investments, fourth in Financial Soundness, and ninth in Global Competitiveness.

It was established by the Federal Housing Enterprises Financial Safety and Soundness Act of 1992.

In the spring of 1863, Lincoln was optimistic about upcoming campaigns to the point of thinking the end of the war could be near if a string of victories could be put together ; these plans included Hooker's attack on Lee north of Richmond, Rosecrans ' on Chattanooga, Grant's on Vicksburg, and a naval assault on Charleston.

Thus, if P is a program in L < sub > 2 </ sub > which is a minimal description of s, then InterpretLanguage ( P ) returns the string s. The length of this description of s is the sum of

The program tries every string, starting with the shortest, until it finds a string with complexity at least n ( if there is one ), then returns that string ( or goes into an infinite loop if there is no such string ).

The twelfth fret divides the string in two exact halves and the 24th fret ( if present ) divides the string in half yet again.

The function F is called universal if the following property holds: for every computable function f of a single variable there is a string w such that for all x, F ( w x ) = f ( x ); here w x represents the concatenation of the two strings w and x.

The tip of the pen will then trace an ellipse if it is moved while keeping the string taut.

Inserting a document using a KSK allows the document to be retrieved and decrypted if and only if the requester knows the human-readable string ; this allows for more convenient ( but less secure ) URIs for users to refer to.

For example, the string GGGAAACCC, if read from the first position, contains the codons GGG, AAA, and CCC ; and, if read from the second position, it contains the codons GGA and AAC ; if read starting from the third position, GAA and ACC.

In the middle position the top wheel pinches the string, resulting in a natural, giving the scale of C major if all pedals are set in the middle position.

In the bottom position another wheel is turned, shortening the string again to create a sharp, giving the scale of C-sharp major if all pedals are set in the bottom position.

Folk harps with levers installed have a lever close to the top of each string ; when it is engaged, it shortens the string so its pitch is raised a semitone, resulting in a sharped note if the string was a natural, or a natural note if the string was a flat.

`` That is, if we can be sure this is Colcord's money '' --

Let me pass over the trip to Sante Fe with something of the same speed which made Mrs. Roebuck `` wonduh if the wahtahm speed limit '' ( 35 m.p.h. ) `` is still in ee-faket ''.

It is the last of the three tests of manhood which the women impose, to discover if a male is worthy of survival there.

There was a measure of protection in its concrete walls and ceiling, but the engineers who hastily installed it were well aware that concrete is not much better than prayer, if as efficacious, when a direct hit comes along.

`` And if the dive goes OK he has the exclusive import rights to your line for this country, is that right ''??

`` All right, if you can't do your arithmetic during school hours you can do it after school is out '', Miss Langford said firmly, not smiling.

Why, in the first place, call himself a liberal if he is against laissez-faire and favors an authoritarian central government with womb-to-tomb controls over everybody??

And if he is so scornful of the rights of states, why not advocate a different sort of constitution that he could more sincerely support??

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

I think it is essential, however, to pinpoint here the difference between the two concepts of sovereignty that went to war in 1861 -- if only to see better how imperative is our need today to clarify completely our far worse confusion on this subject.

Unruly hair goes straight up from his forehead, standing so high that the top falls gently over, as if to show that it really is hair and not bristle.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

He will not curb his instinctual desires but release the energy within him that makes him feel truly and fully alive, even if it is only for this brief moment before the apocalypse of annihilation explodes on earth.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

And if I have gone into so much detail about so small a work, that is because it is also so typical a work, representing the germinal form of a conflict which remains essential in Mann's writing: the crude sketch of Piepsam contains, in its critical, destructive and self-destructive tendencies, much that is enlarged and illuminated in the figures of, for instance, Naphta and Leverkuhn.

All such imitations of negative quality have given rise to a compensatory response in the form of a heroic and highly individualistic humanism: if man can neither know nor love reality as it is, he can at least invent an artistic `` reality '' which is its own world and which can speak to man of purely personal and subjective qualities capable of being known and worthy of being loved.

But Aristotle kept the principle of levels and even augmented it by describing in the Poetics what kinds of character and action must be imitated if the play is to be a vehicle of serious and important human truths.

Operating as a one man police force in fact if not in name, he is at once more independent and more dedicated than the police themselves.