「Proofs」の共起表現(1語右で並び替え)

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rictly formalized mathematical definitions and	proofs, a computer program which is able to check pro
on of computer programs and the formulation of	proofs about program behavior.
His job is to gain	proofs against them and bring them to justice.
rstanding if we were not to provide infallible	proofs and explanations for the truths of the Torah a
y, and Rhodes' doctoral thesis at MIT. Simpler	proofs, and generalizations of the theorem to infinit
vidence along with it, deigns not to submit to	proofs and arguments, but owes the full conviction wi
tion of which you have never ceased to give me	proofs; and wishing upon my part to give you a striki
e Curry-Howard correspondence uses this to map	proofs and computer programs to each other.
Theory of the Earth; with	proofs and illustrations, vol III, Edited by Sir Arch
ows user to define a logic, decide how to view	proofs, and much more.
gebraic and computational and that it eschewed	proofs and rationales.
a meeting with them where he had attended with	proofs and reports of the Pro-French parties actrocit
c framework, filled in gaps, corrected unsound	proofs, and extended the subject in numerous ways.
e findings of 'Proof and Analysis Theory' from	Proofs and Refutations by Hungarian philosopher Imre
resents as sets (called "categories") of their	proofs, and the question of provability became a ques
definitions, heuristic arguments, sketches of	proofs, and the application of powerful analytic meth
hods, the existence of formulae whose shortest	proofs are always superpolynomial has been proved.
These	proofs are commonly known as the "ultraviolet catastr
The	proofs are based on an application of Markov's inequa
cts from deeds, and drawings of seals; but the	proofs are usually taken from private muniments, whic
Dijkstra objected noting that the resulting	proofs are long and cumbersome, and that the proof gi
ed from the book after she had seen the galley	proofs, but was told by the publisher that it was too
e wrote) was accepted and got as far as galley	proofs, but was then removed by demand of other contr
a set of first-order clauses, i.e. it performs	proofs by refutation.
of ordinals, so these cases are often used in	proofs by transfinite induction or definitions by tra
Resulting	proofs can be double-checked by Ivy, a proof-checking
which both computer programs and mathematical	proofs can be expressed.
sign Hume in such a way that formal models and	proofs can definitely be constructed.
In the absence of formal accusations and legal	proofs, composer's reputation was ruined by rumours c
a library and collections of stamps, designs,	proofs, essays and other articles of interest relatin
n, concurrent LP, model checking, bisimilarity	proofs, etc."
Father Spitzer has published New	Proofs for the Existence of God The books authored by
Much subsequent work has gone into alternative	proofs for this formula and into generalized versions
is the process of using software for checking	proofs for correctness.
oratory produced one of the first experimental	proofs for the superfluidity of helium-3.
ts, a few days after correcting the final page	proofs for his New Testament translation.
Harvey of Nedellec's	proofs for the existence of God: de cognitione primi
The theorems were stated without proof, but	proofs for the series for sine, cosine, and inverse t
pia Mathematica, and find new and more elegant	proofs for some.
t this would make it possible to give rigorous	proofs for existing probability results, and he felt
te advanced lung cancer he corrected the final	proofs for his latest encyclopaedia and went to Bath
unnah, whether in life or after death, by many	proofs from our scholars who wrote about it in the bo
	Proofs from THE BOOK, Springer, Berlin, 1998, ISBN 3-
of which you have already given such sterling	proofs, guarantee your future success.
Elementary	proofs have been more recently published.
"direct" proof is possible; allegedly "direct"	proofs have been published, but not everyone agrees t
al knowledge, strictly formalized and with all	proofs having been checked automatically.
additional verification needed for the various	proofs in circulation (cf.
200-6, originally published as Introduction to	Proofs in Mathematics, in 1988.
eaching" that involves exercises in developing	proofs in mathematical logic.
In this case a high degree of automation of	proofs is also possible.
: this is why the question of polynomiality of	proofs is considered important in computational compl
The question of polynomiality of	proofs is whether a method can always produce a proof
ciency of a method in terms of the size of the	proofs it produces.
The corroborative	proofs mooted are: that Tenzin Rabgye was seen (by hi
science, including probabilistically checkable	proofs, non-approximability of optimization problems,
rst method can produce a short proof while all	proofs obtained by the second method are consistently
beral lawyer in a conservative town, reads the	proofs of his son's first novel, set in a fictionaliz
r a set contains a rectifiable subset, and the	proofs of these results frequently depend on β-number
On 6 April 1647 he reported on the some of the	proofs of the Westminster Confession of Faith, and on
as local reasoning, whereby specifications and	proofs of a program component mention only the portio
nish government has given us the most forcible	proofs of its tyranny, its bad faith, and of its inca
special promotion in which a fan could collect	proofs of purchase from the remasters and send them i
From his boyhood he gave	proofs of a strong mathematical bias, and in his latt
stian religion,I told you that besides all the	proofs of it which may be drawn from the prophecies o
James Robison,	Proofs of a Conspiracy (1976).
	Proofs of the Legitimacy of Prince Hall Masonry.
Riemann himself had only given partial	proofs of these statements.
Pappas (1984) gives two	proofs of this theorem.
It was available only via mail by sending in	proofs of purchase to Purina.
Rather, this model is important for its use in	proofs of security against chosen-ciphertext attacks.
	Proofs of his homosexuality exists, everybody knew, e
He knew how to construct	proofs of undeniable originality on many topics in lo
	Proofs of this theorem are given by , and more recent
This book contains one of the first recorded	proofs of the Pythagorean Theorem.
on, Hoffman offers five features and then five	proofs of demolition along with some pointed graphics
press used by the Bedfordshire Times to print	proofs of the front page.
uly 1942, evadees from Auschwitz have provided	proofs of the Holocaust .
oves him, and assuredly shows and demands many	proofs of love" wrote the Queen of Naples.
The composer sent corrected	proofs of the arrangements to the publisher Novello &
Both the Bray and Huisken-Ilmanen	proofs of the Riemannian Penrose inequality state tha
And in 1993 artist's	proofs of his print The Homecoming were the Province'
Niger Coast collection has a number of	proofs of the 1893 issue, some of which are unique.
Cape of Good Hope: Die	proofs of 1d., 6d., and 1s with the rarest item being
His Tazkirahs are considered noble	proofs of his proficiency in everything connected wit
Maybe could be older but there are	proofs of his apperaences in terms of history of Spai
and its architecture is one of the few lasting	proofs of the bygone British Era.
that Merulo used the Steccata's organ for his	proofs of new composition, based on his Venetian expe
Because of this talent, many discoveries and	proofs of other mathematicians became easier to under
nd in enumeration, often providing alternative	proofs of known results.
gave her all sorts of personal privileges and	proofs of affection.
hash functions; bit-commitment; and signature	proofs of knowledge.
Customers could redeem	proofs of purchase from bags of dog food in exchange
and on the difference between purely objective	proofs of Christianity and a subjective relationship
In the first half of 1894, 24	proofs of the Barber series dimes were minted in San
To see some of the early	proofs of one of his prints is to see a study in vivi
the prime number theorem by providing rigorous	proofs of two statements in Bernhard Riemann's semina
Several	proofs of the second kind involve contradictory formu
In number theory, Morton numbers are useful in	proofs, often in examples which map multiple dimensio
then showed, through a series of mathematical	proofs on detailed observational data of the motions
to the definitions proper only, but not to its	proofs or explanations."
	Proofs or constructions using induction and recursion
isting proof, instead of trying to develop new	proofs or theorems itself.
etween the parties were fully disclosed by the	proofs produced, and the court held, after full consi
It is said that having these	proofs proves that the sailor is the champion of all
There have, however, been mathematical	proofs regarding the Biham-Middleton-Levine traffic m
keeping	proofs shorter, by development of appropriate mathema
utomath language for representing mathematical	proofs, so that they could be verified automatically
ermaster file in combination with other secret	proofs such as the Venona intercepts gave US intellig
Of the various philosophical	proofs that he discusses, he singles out the Argument
y I of England, though there aren't historical	proofs that all de Lucys belonged to same family.
lare the law to be that upon the pleadings and	proofs the plaintiff was not entitled to recover; but
on and the Enlightenment ("I look upon logical	proofs the way a well-bred girl looks upon a love let
Sigurd	proofs the sword Gram Johannes Gehrts (1901)
ad prepared the score, he would have been sent	proofs; the conclusion seems inescapable that someone
mathematical abstraction used in cryptographic	proofs; they are typically used when no known impleme
Johnston did not present conclusive	proofs, though he wrote that he had them.
Was it "his duties included delivering	proofs to be approved by artists.."
He found not one correction, only additional	proofs to those very answers originally written witho
ich included manuscripts, notes, revisions and	proofs to all eight of his novels including the Booke
These	proofs use the geometrical properties of reflections
This argument is one of a series of	proofs used to demonstrate that phenomena are without
ounds for the snake-in-the-box problem include	proofs using discrete mathematics and graph theory, e
Simpler	proofs using the inclusion-exclusion principle were g
ethods described was not stressed and, indeed,	proofs were often barely sketched or omitted altogeth
Previously, the page	proofs were printed on oversized paper and driven to
ass of combinatorial arguments, dubbed natural	proofs were unlikely to answer many of the important
on, the DPLL algorithm, etc. produce different	proofs when applied to the same formula.
subject, and for presenting long and difficult	proofs where simple ones are available."
This is especially true in inductive	proofs, where the given expression is taken to be the
	proofs, which are terms whose types are propositions
She is the co-inventor of zero-knowledge	proofs, which probabilistically and interactively dem
esident named Ralph Chapin, who saw the galley	proofs while visiting Japan and, intrigued, asked tha

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