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A generalization of the 0–1 principle for sorting

2005
*
Information Processing Letters
*

*The*traditional zero-one

*principle*

*for*

*sorting*networks states that "if

*a*network with n input lines

*sorts*all 2 n binary sequences into nondecreasing order, then it will

*sort*any arbitrary sequence

*of*... We

*generalize*this to

*the*situation when

*a*network

*sorts*almost all binary sequences and relate it to

*the*behavior

*of*

*the*

*sorting*network on arbitrary inputs. ...

*The*

*generalized*

*0*-

*1*

*principle*has potential benefits

*for*other

*sorting*algorithms and to

*the*best

*of*our knowledge no formal

*generalization*

*of*

*the*

*0*-

*1*

*principle*existed in literature. ...

##
###
A generalization of the zero–one principle for sorting algorithms

1991
*
Discrete Applied Mathematics
*

As

doi:10.1016/0166-218x(91)90050-7
fatcat:fhgqcnxxpvdpfcz5bmo4iyijiq
*a*consequence*a*zero-one*principle**for**a*more*general*class*of**sorting*algorithms is derived. meinschaft under grant Mh 446/*1*-l. 0166-218X/91/$03.50*0*1991 -Elsevier Science Publishers B.V. ... Wagner,*A**generalization**of**the*zero-one*principle**for**sorting*algorithms, Discrete Applied Mathematics 30 (1991) 265-273. ... Moreover, also*for**a*lot*of*new "extensive"*sorting*methods,*for*example parallel*sorting*algorithms [*1*, 3] ,*the*zero-one*principle*turns out to be an invaluable expedient. ...##
###
Designing A Novel General Sorting Network Constructor Using Artificial Evolution

2008
*
Zenodo
*

*A*method is presented

*for*

*the*construction

*of*arbitrary even-input

*sorting*networks exhibiting better properties than

*the*networks created using

*a*conventional technique

*of*

*the*same type. ... Similarly to human inventions in

*the*area

*of*theoretical computer science,

*the*evolved invention was analyzed: its

*generality*was proven and area and time complexities were determined. ... Fig. 5 . 5

*The*

*principle*

*of*creating (k +

*1*)-degree

*sorting*network from

*a*k-degree

*sorting*network

*a*)

*a*2k+

*1*=

*0*and

*a*2k+2 =

*0*Fig. 6 . 6 Processing data sequences: (

*a*)

*a*2k+

*1*=

*0*,

*a*2k+2 =

*0*, (b) ...

##
###
Evolutionary Design of Arbitrarily Large Sorting Networks Using Development

2005
*
Genetic Programming and Evolvable Machines
*

*The*proposed approach allowed us to rediscover

*the*conventional

*principle*

*of*insertion which is traditionally used

*for*constructing large

*sorting*networks. ... Furthermore,

*the*

*principle*was improved by means

*of*

*the*evolutionary technique.

*The*evolved

*sorting*networks exhibit

*a*lower implementation cost and delay. ... Acknowledgements

*The*research was performed with

*the*Grant Agency

*of*

*the*Czech Republic under No. 102/03/P004 Evolvable hardware based application design methods and No. 102/04/0737 Modern methods

*of*digital ...

##
###
Combinatorial Techniques for Proof-Based Synthesis of Sorting Algorithms

2015
*
2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)
*

We present

doi:10.1109/synasc.2015.30
dblp:conf/synasc/DramnescJS15
fatcat:zfymky4kifgbtpb5oboskj35je
*the*main*principles*and*the*application*of*this technique to merging*of**sorted*binary trees into*a**sorted*one. ... In*the*frame*of*our previous experiments*for*proof based synthesis*of**sorting*algorithms*for*lists and*for*binary trees, we employed certain special techniques which are able to*generate*multiple variants ... Since each such expression must represent*a**sorted*tree,*generate**for*each expression*the*corresponding condition as*a*set*of*microatoms (see IR-*1*). ...##
###
Optimal conclusive sets for comparator networks

2009
*
Theoretical Computer Science
*

Nakatani et. al. [11] used it to prove

doi:10.1016/j.tcs.2008.12.021
fatcat:iew336oxczfflncennm6lvaxqe
*the*correctness*of**a*bitonic sorter. Rajasekaran and Sen [12]*generalized**the**0*-*1**principle*to networks that*sort*almost all*0*-*1*inputs. ... Miltarsen et. al. [10] used*a*variant*of**the**0*-*1**principle*to prove*the*correctness*of**a*merging network. ... Acknowledgments We thank Tuvi Etzion*for**the*suggestion to use Sperner's Theorem in*the*proof*of*Theorem 15. ...##
###
Proof–Based Synthesis of Sorting Algorithms for Trees
[chapter]

2016
*
Lecture Notes in Computer Science
*

We develop various proof techniques

doi:10.1007/978-3-319-30000-9_43
fatcat:e7lnwtt2l5cn7igumgimb5hsbe
*for**the*synthesis*of**sorting*algorithms on binary trees, by extending our previous work on*the*synthesis*of*algorithms on lists. ...*The*proof techniques are implemented in*the*Theorema system and are used*for**the*automatic synthesis*of*several algorithms*for**sorting*and*for**the*auxiliary functions, from which we present few here. ... This*generates**the*same conjecture*for**the*synthesis*of*Merge and also*the*last branch in*the*following*sorting*algorithm, knowing that if*the*proof succeeds to find*a*witness T * = [n, L*0*, R*0*, T*1*...##
###
Proof–Based Synthesis of Sorting Algorithms Using Multisets in Theorema

2019
*
Electronic Proceedings in Theoretical Computer Science
*

We use

doi:10.4204/eptcs.303.6
fatcat:igy2uupkjndwrduuyewqndufo4
*the*classical*principle**of*extracting*the*algorithm as*a*set*of*rewrite rules based on*the*witnesses found in*the*proof*of**the*synthesis conjecture produced from*the*specification*of**the*desired ... Using multisets, we develop novel techniques*for*mechanizing*the*proofs*of**the*synthesis conjectures*for*list-*sorting*algorithms, and we demonstrate them in*the*Theorema system. ... (*For*lack*of*space we omit here*a*possible splitting algorithm and its automatic*generation*by*the**principles*presented in this paper.) ...##
###
Order-Sorted Inductive Types

1999
*
Information and Computation
*

Decidability

doi:10.1006/inco.1998.2751
fatcat:ltlehlcvnrgnhkmppmwijpg4zm
*of*subtyping Decidability*of*subtyping, which constitutes*the*most intricate part*of**the*proof*of*decidability*of*type-checking, is typically established in four steps Com95, PS97]: ... is an extension*of*system F ! with subtyping and bounded quanti cation. Order-*sorted*algebra is an extension*of*many-*sorted*algebra with overloading and subtyping. ... Earlier versions*of**the*paper were written while*the*author was working at*the*Center*for*Mathematics and Computer Science (CWI), Amsterdam, and Chalmers University, G oteborg. ...##
###
Making sense of snapshot data: ergodic principle for clonal cell populations

2017
*
Journal of the Royal Society Interface
*

In

doi:10.1098/rsif.2017.0467
pmid:29187636
pmcid:PMC5721154
fatcat:h4uokabczfcgtj4a3yic4ugodm
*the*presence*of**generation*time variability,*the*average acquired across*a*population snapshot does not obey*the*average*of**a*dividing cell over time, apparently contradicting ergodicity between single ...*The*correspondence between cells*of*known age in*a*population with their histories represents an ergodic*principle*that provides*a*new interpretation*of*population snapshot data. ... It is*a*pleasure to thank Diego Oyarzú n and Vahid Shahrezaei*for*valuable feedback. ...##
###
AN 11-STEP SORTING NETWORK FOR 18 ELEMENTS

2009
*
Parallel Processing Letters
*

However,

doi:10.1142/s0129626409000092
fatcat:2rn6lvlrkvcolf2hh6hf7mqjfi
*the*fastest implementable*sorting*networks built so far consume Θ(Nlog 2 N) comparisons, and*generally*, use*the*Merge-*sorting*strategy to*sort**the*input. ... An 18-element network using*the*Merge-*sorting*strategy needs at least 12 steps-here we show*a*network that*sorts*18 elements in only 11 steps. ... Figure 2 illustrates*a*typical Knuth diagram*for**sorting*4 elements [5] .*The**0*/*1**principle**The**0*/*1**principle*plays*a*vital role in building and verifying*sorting*networks. ...##
###
Research on the SDIF Failure Principle for RF Stealth Radar Signal Design

2022
*
Electronics
*

*The*

*principle*

*of*SDIF

*sorting*threshold failure provides theoretical support

*for*anti-

*sorting*RF stealth signal design. ... Theoretically speaking,

*the*anti-

*sorting*signal design is based on

*the*failure

*principle*

*of*

*the*radar signal

*sorting*algorithm, and

*the*SDIF algorithm is

*a*core

*sorting*algorithm widely used in engineering ...

*The*

*sorting*failure

*principle*provides theoretical support

*for*

*the*design

*of*anti-

*sorting*signals and helps to improve

*the*efficiency and success rate

*of*signal anti-

*sorting*design. ...

##
###
Accelerating certain outputs of merging and sorting networks

2009
*
Theoretical Computer Science
*

An additional contribution

doi:10.1016/j.tcs.2009.04.024
fatcat:evo7ukrtrzgcrf3sybz6evmi2a
*of*this paper concerns*the*well-known*0*-*1**Principle*[D.E. Knuth,*The*Art*of*Computer Programming vol. 3:*Sorting*and Searching, second edition, Addison-Wesley, 1998]. ... In*the*case at hand, this new tool simplifies one*of*our proofs by having fewer special cases than*the*classical*0*-*1**Principle*.*A*second additional contribution concerns Batcher's merging techniques. ...*A*powerful tool*for*studying merging networks, similar to*the**0*-*1**Principle*, is*the*set*of*Sandwich vectors, presented in [4] . ...##
###
On Computable Numbers, Nonuniversality, and the Genuine Power of Parallelism
[chapter]

2016
*
Emergent Computation
*

To illustrate, consider

doi:10.1007/978-3-319-46376-6_4
fatcat:bwg7tkpgtnhypk72bgbmpivwcu
*the*following parallel algorithm*for**sorting**a*sequence S = g*0*, g*1*, . . . , g n−*1**of*n distinct integers on*a*linear array*of*processors p*0*, p*1*, . . . , p n−*1*. ... Parallel*Sort**for*k =*0*to n −*1*do*for*i =*0*to n − 2 do in parallel if i mod 2 = k mod 2 then p i and p i+*1*compare and swap if needed end if end*for*end*for*. ... Perspicuously stated, it says that*a*function is Algorithm Sequential*Sort*completes*the**sort*in O(n 2 ) time (clearly not*the*best*sorting*algorithm sequentially, but*a*sufficient illustration*of**the*...##
###
A Currentless Sorting and Selection based Capacitor-Voltage-Balancing Method for Modular Multilevel Converters

2018
*
IEEE transactions on power electronics
*

This letter proposes

doi:10.1109/tpel.2018.2850360
fatcat:fidhttqhxrawrilkvawkmwa5cq
*a*currentless*sorting*and selection (SAS) based capacitor-voltage-balancing method*for*modular multilevel converters (MMCs). ... In this letter,*the*derivative*of**the*total capacitor voltage*of*an arm, instead*of**the*arm current, is employed to determine which sub-modules (SMs) should be inserted or bypassed. ... CONCLUSION Table I Two I states*of**a*half-bridge SM State T1H T2H Inserted on off*1*Bypassed off on*0*To investigate*the*working*principles**of*an MMC, mathematical relationships*of*different ...
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