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## Filters

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The probability of pure literals

1999
*
Journal of Logic and Computation
*

Speci cally, we show with

doi:10.1093/logcom/9.4.501
fatcat:4b5gr4bitffbzb3swibetv3vxu
*probability*approaching 1 as m goes to 1 one can apply*the**pure**literal*rule repeatedly to a random instance*of*2-SAT until*the*number*of*clauses is \small" provided n=m > 1. ... We describe an error in earlier probabilistic analyses*of**the**pure**literal*heuristic as a procedure for solving k-SAT. ...*probability**the*sum*of**the*lengths*of*all cycles*of*C is at least t and no cycles*of*C are connected is phenomenal success*of**the**pure**literal*heuristic under*the*hypotheses*of*Theorem 3.3 it is reasonable ...##
###
Average time for the full pure literal rule

1994
*
Information Sciences
*

*The*random problems are characterized by t h e n umber

*of*variables v,

*the*number

*of*clauses t, and

*the*

*probability*that a

*literal*is in a clause p. ...

*The*simpli ed

*pure*

*literal*algorithm solves satis ability problems by c hoosing variables in a xed order and then generating subproblems for various values

*of*

*the*chosen variable. ... Extensive assistance

*of*Professor Khaled Bugrara with this research is greatly appreciated. I also wish to thank Northeastern university for

*the*use

*of*computer resources for some

*of*

*the*...

##
###
A sharp threshold in proof complexity

2001
*
Proceedings of the thirty-third annual ACM symposium on Theory of computing - STOC '01
*

We give

doi:10.1145/380752.380820
dblp:conf/stoc/AchlioptasBM01
fatcat:tonk7hhnbffmxa6w2qdgaescmy
*the*first example*of*a sharp threshold in proof complexity. ... A consequence*of*our result also yields*the*first proof that typical random 3-CNF formulas at ratios below*the*generally accepted range*of**the*satisfiability threshold (and thus expected to be satisfiable ... Define*the*set È È´Àµ*of**literals*based on À as follows: È consists*of**the**pure**literals**of*À¾,*the*smallest numbered*literal*in each*pure*cycle*of*À¾, and every*literal*on*the*variables*of*Î´Àµ Î´À¾µ. ...##
###
Linear Upper Bounds for Random Walk on Small Density Random 3‐CNFs

2007
*
SIAM journal on computing (Print)
*

We use

doi:10.1137/s0097539704440107
fatcat:25poeogesfez3geamwbmbdvpqy
*the*analysis*of**the**pure**literal*heuristic presented by Broder, Frieze, and Upfal [show that for small clause densities good terminators exist. ... Thus we show that*the**pure**literal*threshold (≈1.63) is a lower bound on*the*terminator threshold. (We conjecture*the*terminator threshold to be in fact higher.) ... We thank Bart Selman and Andrew Parkes for valuable information on*the*empirical results regarding RWalkSAT and Balint Virag for his help with*the*analysis*of*martingales. ...##
###
Hard satisfiable formulas for DPLL-type algorithms
[article]

2003
*
arXiv
*
pre-print

Namely, we consider two DPLL-type algorithms, enhanced with

arXiv:cs/0301012v1
fatcat:fsrof6akyjabnnjmcvkoxmje4m
*the*unit clause and*pure**literal*heuristics. ... We address lower bounds on*the*time complexity*of*algorithms solving*the*propositional satisfiability problem. ... Hirsch, who suggested*the*problem and supervised my work. ...##
###
Structure of random r-SAT below the pure literal threshold
[article]

2010
*
arXiv
*
pre-print

It remains open what happens between

arXiv:1008.1260v1
fatcat:cnsmnzdinbe67alq3l5fckpo74
*the**pure**literal*threshold and*the*satisfiability threshold. ... By contrast, we show that for*the*(rare) unsatisfiable formulae below*the**pure**literal*threshold,*the*unsatisfiability is whp due to a unique MUF with smallest possible "excess", failing this whp due to ... ), and a similar asymptotic expansion for*the**probability*that*the**pure**literal*rule fails. ...##
###
A sharp threshold in proof complexity yields lower bounds for satisfiability search

2004
*
Journal of computer and system sciences (Print)
*

Our result also yields

doi:10.1016/j.jcss.2003.07.011
fatcat:rbnd5tlzynaa3ffenstwa7cpfy
*the*first proof that random 3-CNF formulas with densities well below*the*generally accepted range*of**the*satisfiability threshold (and thus believed to be satisfiable) cause natural ... Let F ðrn; DnÞ denote a random CNF formula consisting*of*rn randomly chosen 2-clauses and Dn randomly chosen 3-clauses, for some arbitrary constants r; DX0: It is well-known that, with*probability*1 À ...*probability*that F Ã has a small subformula H with few*pure*items by bounding*the**probability*for each set*of**literals*T that there is a subformula H*of*F Ã with P Ã ðHÞ ¼ T and with at most jTj=10*pure*...##
###
Page 539 of None Vol. 83, Issue
[page]

1927
*
None
*

*The*usual result

*probably*contains something

*of*both:

*the*original representative (or realistic; or impression- istic!) element being present, but subjected to a

*purely*musical destiny. ... Beethoven’s sixth and seventh symphonies are clearly on

*the*edge, if not

*of*

*the*

*literal*, then

*of*

*the*metaphorical. ...

##
###
Results related to threshold phenomena research in satisfiability: lower bounds

2001
*
Theoretical Computer Science
*

., this volume)

doi:10.1016/s0304-3975(01)00158-x
fatcat:zo4zevfstfakflhhjdxq4lrnsa
*the*major ideas used to achieve many*of**the*lower bounds results on*the*location*of**the*threshold are described in an informal, intuitive manner. ... We present a history*of*results related to*the*threshold phenomena which arise in*the*study*of*random conjunctive normal form (CNF) formulas. In a companion paper (D. Achlioptas, Theoret. Comput. ... Formula (1) is said to be*the*result*of*an application*of**the*unit clause rule in*the*former case and an application*of**the**pure**literal*rule in*the*latter case. ...##
###
Page 101 of Journal of Chemical Physics Vol. 35, Issue 1
[page]

1961
*
Journal of Chemical Physics
*

This may

*probably*be due to*the*greater concentration quenching that results from*the*much lower viscosity*of**pure*anisole as compared to anisole in paraffin oil. ... (e) Variation*of*viscosity with temperature*of*solutions*of*0.5 g/*liter*anthracene in mixtures*of*anisole and paraffin oil. Curve (1):*pure*anisole. ...##
###
On smoothedk-CNF formulas and the Walksat algorithm
[chapter]

2009
*
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
*

Starting from an arbitrary instance F with n variables and m = dn clauses, apply

doi:10.1137/1.9781611973068.50
fatcat:cwlphlosyzc4dnx3ev33gorfte
*the*ε-smoothing operation*of*flipping*the*polarity*of*every*literal*in every clause independently at random with*probability*... In this paper we study*the*model*of*ε-smoothed k-CNF formulas. ... Hence,*the**probability*that there is a set S*of*size s with µ clauses and without a*pure**literal*is at most s ≤ e s n k−1 km n µ . ...##
###
Page 331 of The Antijacobin Review and Protestant Advocate, Or, Monthly Political, and Literary Censor Vol. 41, Issue
[page]

1812
*
The Antijacobin Review and Protestant Advocate, Or, Monthly Political, and Literary Censor
*

if it be not generally

*the*land*of*delights, is at least within*the*Jand*of*delights, a part*of**the*whole, and*probably**the*capital, and*probably**the*Mount Sion, that joy*of**the*whole earth, within that ... As these enemies are thus, however, gathered toa war, there must be a hostile force on*the**pure*side: there must be, at this time, some*pure*power,*of*such growing consequence as to require these extraordinary ...##
###
Page 210 of Rubber Chemistry and Technology Vol. 1, Issue 2
[page]

1928
*
Rubber Chemistry and Technology
*

Eight gallons (36

*liters*)*of**the*railway hydro- carbon gave a little over a*liter**of*these hydrocarbons, from which about 200 grams*of**the*crude solid tetrabromide and 145 grams*of**the*liquid tetrabromides ... Preparation*of**Pure*Butadiene*Pure*butadiene can be readily and conveniently prepared from*the*solid tetrabromide by*the*method described by Thiele.2 For most purposes*the*once-crystallized material is ...##
###
Attached growth of Sphaerotilus and mixed populations in a continuous-flow apparatus

1968
*
Applied microbiology
*

*The*effects

*of*NH(4)Cl concentration, organic nitrogen compounds, glucose concentration, dissolved oxygen concentration, and flow rate on

*the*attached growth

*of*

*pure*cultures

*of*Sphaerotilus natans and ...

*The*conditions that allowed maximal attached growth in

*pure*culture did not correspond to

*the*conditions that promoted attached growth

*of*Sphaerotilus in a mixed population. ... However,

*the*open channels used by most investigators

*probably*are more difficult to control and are difficult, if not impossible, to use for

*pure*-culture studies. ...

##
###
THE QUANTITATIVE DETERMINATION OF CHLOROPHYLL

1928
*
Plant Physiology
*

*PROBABLE*ERROR

*OF*A SINGLE DETERMINATION CONCENTRATION IN GRAMS PER

*LITER*0.20 0.15 0.10 0.05 mm. ... Calculating, using

*the*values for grams

*of*From

*the*curve in fig. 1 , these readings are interpreted in terms

*of*grams

*of*chlorophyll per

*liter*respectively as follows:

*The*

*probable*error

*of*a single ...

*The*spectrophotometric method offers great promise

*of*being a very accurate method for determining chlorophyll, though

*the*data for

*the*method are yet to be obtained. LITERATURE CITED ...

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