In literature:
Dig a pit in the middle of that track, and when Fafnir comes over it strike up into his coils of mail with Gram, thy great sword.
"The Children of Odin" by Padraic Colum
Flashlights probed into the hot impact pit in the open field, where the frozen soil had seemed to splash like a liquid.
"The Planet Strappers" by Raymond Zinke Gallun
The water is accumulated in this pit until it is filled, then it will automatically empty itself as later explained.
"Elements of Plumbing" by Samuel Dibble
The boiler pit is located in a sunken shed outside, not shown in the plan.
"Woodward's Graperies and Horticultural Buildings" by George E. Woodward
Chanting a loud, monotonous chorus, the natives threw themselves into the work and speedily had three pits started.
"The Rogue Elephant" by Elliott Whitney
At his side was a thin man with a face pitted by smallpox, and a forehead covered with strange protuberances.
"The Manxman A Novel - 1895" by Hall Caine
They soon got back to the pit-fall, Guapo of course leading the way.
"Popular Adventure Tales" by Mayne Reid
Pitting very slightly raised his voice.
"Tongues of Conscience" by Robert Smythe Hichens
The meeting was over, and the boys went in twos and threes from the shed discussing the forthcoming battle in the sand-pit.
"The Hero of Garside School" by J. Harwood Panting
Come to the pit when the Baron is safe in the house.
"The Dragon of Wantley" by Owen Wister
Snowflake's heart went pit-a-pat, pit-a-pat, when she saw the reindeer.
"The Later Cave-Men" by Katharine Elizabeth Dopp
At midnight to-night, come here to the cottage, for I want you to help me to carry the body into the woods to the quicksand pit.
"A Woman at Bay" by Nicholas Carter
He was played by the low-comedian, who had introduced gags of his own and was on most friendly terms with the pit.
"The Picture of Dorian Gray" by Oscar Wilde
Then he saw how easily it would be to escape observation by falling into the small pit.
"The Boy Ranchers on Roaring River" by Willard F. Baker
At Layroh's order the men entered the floor-pits, one man to each pit.
"The Cavern of the Shining Ones" by Hal K. Wells
Now that the danger had passed, Larkin felt a certain miserable nausea in the pit of his stomach, and fought it down with all his might.
"The Free Range" by Francis William Sullivan
Then the turnips were pitted and work was slack.
"The Rainbow" by D. H. (David Herbert) Lawrence
Margin very much incurved, stem pitted.
"The Mushroom, Edible and Otherwise" by M. E. Hard
He ordered me to be thrown into one of the great pits in the inner gardens.
"The Gods of Mars" by Edgar Rice Burroughs
He was a man of middle size, perhaps fifty, bald, and wearing an old leather skull-cap pitted with spark holes.
"Dwellers in the Hills" by Melville Davisson Post
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In poetry:
The plaïn ha' brightness wi' his strife,
The pit is only dark at best,
There's pleasure in a worksome life,
An' sloth is tiresome wi' its rest.
"Thissledown" by William Barnes
I will not fall! I will not; thou dost lie!
Deep Hell! that seethest in thy simmering pit;
Thy thousand throned horrors shall not vie,
Or ever compass it!
"Aspiration" by Madison Julius Cawein
Enoch, because he truly serv'd the Lord,
Never descended to the pit beneath —
But, in the flesh, to joys celestial soar'd,
Before he saw the dreary form of Death.
"Advice To Serve God" by Rees Prichard
Forgive my faults, allay this raging smart,
And save me from th' unfathom'd pit of hell,
That I may worship thee with all my heart,
And, whilst I live, thy boundless praises tell.
"Another On The Same Subject " by Rees Prichard
Something more than butterflies,
Or the sugared ancient lies,
Something with the ring of truth,
And the majesty of youth,
Something singing "all is well"
In the blackest pit of hell!
"A Song of Singers" by Richard Le Gallienne
Then all to your Saviour together repair,
To save your lost souls from the pit of despair;
Whoe'er will come freely in heaven shall dwell:
But all, who refuse, shall be tumbled to hell.
"Another Piece Of Advice To Sinners To Come To Christ" by Rees Prichard
In news:
A 3-month-old baby boy died Monday night after being mauled by the family's pit bull.
4 attacked by pit bull at doggie daycare.
A bride is recovering from injuries after she was attacked by a pit bull mix and its owner at her wedding reception.
A landlord was attacked by a pit bull Thursday afternoon during a visit to a tenant's home on Rushin Drive, Athens-Clarke police said.
Pit bull attacks girl, 7.
A 7-year-old girl was attacked yesterday by a pit bull in a hallway of an East Harlem housing project.
A Terryville woman is recovering after she was bit by a Pit Bull over the weekend.
Boy Bitten By Pit Bull In Oxnard Will Have To Undergo Painful Rabies Shots If Dog Isn't Found.
Brothers Mauled by Pit Bulls Discuss Recovery.
A Rockville woman was hospitalized Thursday afternoon after she was attacked by a pit bull.
Pit bulls are landing in Maricopa County animal shelters in droves, and they are staying the longest and getting euthanized more often than other breeds, shelter officials said.
An unprecedented 14,523 pit bulls filled Maricopa County shelters last year, making up about one-third of the shelters' dog population.
A 5-year-old pony had to be put to sleep Wednesday after it was attacked by two pit bulls.
Learning the Ropes, Pit Stop by Pit Stop.
The joke about the driver who made a dozen pit stops at the Indianapolis 500 to ask for directions is not as absurd as it sounds, once you talk to Scott Pruett.
***
In science:
The equivalence further shows that PIT of depth 3 arithmetic circuits reduces to PIT of width-2 planar commutative Algebraic Branching Programs (ABP).
The Power of Depth 2 Circuits over Algebras
Polynomial identity testing (PIT) is a fundamental problem in theoretical computer science.
The Power of Depth 2 Circuits over Algebras
As such, no other general polynomial time result is known for depth 3 circuits. A justiﬁcation behind the hardness of PIT even for small depth circuits was provided recently by Agrawal and Vinay [AV08].
The Power of Depth 2 Circuits over Algebras
They showed that a deterministic black box identity test for depth 4 (ΣΠΣΠ) circuits would imply a quasi-polynomial time deterministic PIT algorithm for any circuit computing a polynomial of low degree1 .
The Power of Depth 2 Circuits over Algebras
Thus solving Problem 1.3 in polynomial time even for 3 × 3 matrices yields a polynomial time algorithm for PIT of constant depth circuits, in particular depth 4 circuits.
The Power of Depth 2 Circuits over Algebras
Thus, PIT for depth 2 circuits over 3 × 3 matrices is almost the general case since a derandomization yields a quasi-polynomial time PIT algorithm for any circuit computing a low degree polynomial.
The Power of Depth 2 Circuits over Algebras
The other direction, that is PIT for depth 2 circuits over U2 (F) reduces to PIT for depth 3 circuits, is trivial to observe.
The Power of Depth 2 Circuits over Algebras
As a matter of fact, the above argument actually shows that PIT of depth 2 circuits over M2 (F) reduces to PIT of width-2 ABPs.
The Power of Depth 2 Circuits over Algebras
It is a central question in complexity theory as circuits model computation and PIT leads us to a better understanding of circuits.
Algebraic Independence and Blackbox Identity Testing
Derandomization of PIT is well motivated by a host of algorithmic applications, eg. bipartite matching [Lov79] and matrix completion [Lov89], and connections to sought-after super-polynomial lower bounds [HS80, KI04].
Algebraic Independence and Blackbox Identity Testing
The attempts to solve blackbox PIT have focused on restricted circuit families. A natural restriction is constant depth.
Algebraic Independence and Blackbox Identity Testing
Agrawal & Vinay [AV08] showed that a blackbox PIT algorithm for depth-4 circuits would (almost) solve PIT for general circuits (and prove exponential circuit lower bounds for permanent).
Algebraic Independence and Blackbox Identity Testing
The currently known blackbox PIT algorithms work only for further restricted depth-3 and depth-4 circuits.
Algebraic Independence and Blackbox Identity Testing
However, with the additional restriction of multilinearity on all the multiplication gates, there is a blackbox PIT algorithm [KMSV10, SV11].
Algebraic Independence and Blackbox Identity Testing
The latter is somewhat subsumed by the PIT algorithms for constant-read multilinear formulas [AvMV10].
Algebraic Independence and Blackbox Identity Testing
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