There is no independent clause or sentence which prohibits the States from exercising it.
"The Federalist Papers" by Alexander Hamilton, John Jay, and James Madison
The personal pronoun is sometimes omitted in subordinate and even independent clauses; cf.
"Beowulf" by Unknown
Subjunctive in Independent Clauses.
"An English Grammar" by W. M. Baskervill and J. W. Sewell
The complex sentence contains one independent clause and at least one subordinate clause.
"Public Speaking" by Clarence Stratton
Between two independent clauses connected by a conjunction.
"Punctuation" by Frederick W. Hamilton
When a sentence consists of two or more independent clauses not joined by conjunctions, the clauses are separated by semicolons.
""Stops"" by Paul Allardyce
By what are independent clauses connected?
"Practical Grammar and Composition" by Thomas Wood
Dependent clauses preceded by "that" should be kept distinct from those that are independent.
"How to Write Clearly" by Edwin A. Abbott
Declaration of Independence, clause in regarding wrongs of slave trade suppressed, 9.
"The Negro and the Nation" by George S. Merriam
And last, if it deserves such a distinction, the thought may demand an independent clause or a sentence for itself.
"English: Composition and Literature" by W. F. (William Franklin) Webster
The clause in the agreement between Serbia and Bulgaria, providing for an independent Macedonia, is especially significant.
"The Story of the Great War, Volume I (of 8)" by Various
In the following quotation, mark all of the clauses and determine whether they are dependent or independent clauses.
"Plain English" by Marian Wharton
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Generating Φd is equivalent to drawing a random bijection π : [m] × [k ] → B , with π(i, j ) = (x, l) indicating that x is the underlying variable of the j th literal of clause i, and independently choosing a map s : [m] × [k ] → {±1} indicating the signs.
Catching the k-NAESAT Threshold
Therefore, given that σ ∈ Sβ (Φ), the variables that occur in the non-critical clauses are independent and uniformly distributed over the set of all variables.
Catching the k-NAESAT Threshold
Similarly, given that σ ∈ Sβ (Φ) the k − 1 variables that contributed the “majority value” to each critical clause are independently uniformly distributed.
Catching the k-NAESAT Threshold
P [(f , tred ∪ tblue ) is valid for s] is that in the underlying random experiment, the clauses are independent objects, although there are different “types” of clauses.
Catching the k-NAESAT Threshold
First of all, their selection may either be chosen independently for all slots (i.e., allowing a clause to contain more than one slot with the same variable), or indepdently for all slots but conditioning on the k variables occuring in a clause being distinct.
On the satisfiability of random regular signed SAT formulas
To see that such a run r (cid:48) indeed exists in Rmax , we note that clause (ii) relates to nodes outside past(r, (ik , t(cid:48) )) and thus by assumption does not contradict clause (i), and that by deﬁnition all early message receives can be delayed, independent of the run’s past or concurrent events.
Causality, Knowledge and Coordination in Distributed Systems
Note that the variables appearing in each clause are independent and uniformly random.
The Power of Choice for Random Satisfiability
In particular, this shufﬂing occurs independently for each clause type.
Going after the k-SAT Threshold
Furthermore, these events are independent (because the clauses Cx were disregarded in the construction of R).
Going after the k-SAT Threshold
We can generate a pair (Φ, σ) from the planted model as follows: ﬁrst, choose σ ∈ {0, 1}V uniformly; then, generate m clauses that are satisﬁed under σ uniformly and independently.
Going after the k-SAT Threshold
Then, conditional on Nt , the clauses of Φt are random and independent.
The phase transition in random Horn satisfiability and its algorithmic implications
Then for every stage t, conditional on Γt = (H N1,t , H N2,t , H P1,t , H P2,t , Et ) the clauses of Φt are chosen uniformly at random and are independent. 3.
The phase transition in random Horn satisfiability and its algorithmic implications
Given the uniformity in the choice of the initial clauses of Φ, it follows that the clauses of Φt are chosen uniformly at random (and independently) among all nonempty Horn clauses in the remaining variables. 2.
The phase transition in random Horn satisfiability and its algorithmic implications
Lemma 4.1 (ii); we only use the superscript to indicate the fact that we are dealing with a different algorithm) the clauses of Φt denote their number by N (2) ) are uniform and independent.
The phase transition in random Horn satisfiability and its algorithmic implications
We modify this process to also place, at each stage j such that H P1,j > 0, some blue pebbles on the piles corresponding to negative non-unit clauses, at follows: each such clause that has no pebble on it independently receives a blue pebble with probability 1/j .
The phase transition in random Horn satisfiability and its algorithmic implications
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