Key compiler algorithms (for embedded systems)
|
|
|
- Magdalene Green
- 6 years ago
- Views:
Transcription
1 Key ompiler lgorithms (for emee systems) Peter Mrweel University of Dortmun, Germny P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri
2 Universität Dortmun Opertions/Wtt [MOPS/mW].0µ ASIC Reonfigurle Computing Proessors 0.µ 0.2µ Motivtion: Wishes n Relity Amient Intelligene 0.3µ Avoi poor esign tehniques! 0.07µ Tehnology P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Results for DSPStone enhmrk Cyle overhe [ n] TIC ADI20 DSP600 Fri 2
3 Reson for ompilerprolems: Applitionoriente Arhitetures Applition: u..: y[j] = i=0 x[ji]*[i] i: 0 i n: y i [j] = y i [j] x[ji]*[i] Arhiteture: Exmple: Dt pth ADSP20x D x P n Aressregisters A0, A, A2.. i, ji Aress genertion unit (AGU) AX AY,,.. AR AF x[ji] MX *, MR MY [i] MF x[ji]*[i] y i [j] Prllelism Deite registers No mthing ompiler ineffiient oe P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 3
4 Exploittion of prllel ress omputtions Aress Register File Generi ress genertion unit (AGU) moel Instrution Fiel Memory / Moify Register File P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Prmeters: k = # ress registers m = # moify registers Cost metri for AGU opertions: Opertion Fri 4 ost immeite AR lo immeite AR moify utoinrement/ 0 erement AR = MR 0
5 Aress pointer ssignment (APA) Given: Memory lyout ssemly oe (without ress oe) r i r i lt r mpy r ltp i mpy r sl r ltp i mpy r p sl r How to ess r? time Aress pointer ssignment (APA) is the suprolem of fining n llotion of ress registers for given memory lyout n given sheule. P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri
6 Generl pproh: Minimum Cost Cirultion Prolem Let G = (V,E,u,), with (V,E): irete grph u: E R 0 is pity funtion, : E R is ost funtion; n = V, m = E. Definition: g: E R 0 is lle irultion if it stisfies : v V: w V:(v,w) E g(v,w)= w V:(w,v) E g(w,v) (flow onservtion) g is fesile if (v,w) E: g(v,w) u(v,w) (pity onstrints) The ost of irultion g is (g) = (v,w) E (v,w) g(v,w). There my e lower oun on the flow through n ege. The minimum ost irultion prolem is to fin fesile irultion of minimum ost. [K.D. Wyne: A Polynomil Comintoril Algorithm for Generlize Minimum Cost Flow, ~wyne/ ppers/ rtio.pf] P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 6
7 Mpping APA to the Minimum Cost Cirultion Prolem Assemly sequene* lt r mpy r ltp i mpy i mpy r sl r ltp i mpy r p time sl r AR S u(t S)= AR AR2 Flow into n out of vrile noes must e. Reple vrile noes y ege with lower oun= to otin pure irultion prolem irultion selete itionl eges of originl grph (only smples shown) * C2x proessor from ti Vriles T i r r i resses [C. Geotys: DSP Aress Optimiztion Using A Minimum Cost Cirultion Tehnique, ICCAD, 997] P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 7
8 Results oring to Geotys Optimize oe size Originl oe size Limite to si loks P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 8
9 Beyon si loks: hnling rry referenes in loops Exmple: for (i=2; i<=n; i) {.. B[i] /*A2 */.. B[i] /*A */.. B[i2] /*A2 */.. B[i] /*A */.. B[i3] /*A2 */.. B[i] } /*A */ Cost for rossing loop ounries onsiere. Referene: A. Bsu, R. Leupers, P. Mrweel: Arry Inex Allotion uner Register Constrints, Int. Conf. on VLSI Design, Go/Ini, 999 Control steps Offsets P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, A X X X X A2 X X X Fri 9 X X
10 Offset ssignment prolem (OA) Effet of optimise memory lyout Let's ssume tht we n moify the memory lyout offset ssignment prolem. (k,m,r)oa is the prolem of generting memory lyout whih minimizes the ost of ressing vriles, with k: numer of ress registers m: numer of moify registers r: the offset rnge The se (,0,) is lle simple offset ssignment (SOA), the se (k,0,) is lle generl offset ssignment (GOA). P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 0
11 SOA exmple Effet of optimise memory lyout Vriles in si lok: Aess sequene: V = {,,, } S = (,,,,, ) Lo AR, ; AR = 2 ; AR = 3 ; AR = 2 ; AR ; AR ; Lo AR,0 ; AR ; AR =2 ; AR ; AR ; AR ; ost: 4 ost: 2 P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri
12 SOA exmple: Aess sequene, ess grph n Hmiltonin pths ess sequene: 2 ess grph 2 mximum weighte pth= mx. weighte Hmilton pth overing (MW HC) memory lyout SOA use s uiling lok for more omplex situtions signifint interest in goo SOA lgorithms P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 [Brtley, 992; Lio, 99] Fri 2
13 Nïve SOA Noes re e in the orer in whih they re use in the progrm. Exmple: Aess sequene: S = (,,,,, ) memory lyout P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 3
14 Lio s lgorithm Similr to Kruskl s spnning tree lgorithms:. Sort eges of ess grph G=(V,E) oring to their weight 2. Construt new grph G =(V,E ), strting with E =0 3. Selet n ege e of G of highest weight; If this ege oes not use yle in G n oes not use ny noe in G to hve egree > 2 then this noe to E otherwise isr e. 4. Goto 3 s long s not ll eges from G hve een selete n s long s G hs less thn the mximum numer of eges ( V ). Exmple: Aess sequene: S=(,,,,, ) Impliit eges of weight 0 for ll unonnete noes. G 2 2 (,) (,) (,) (,) P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, G 2 Fri 4
15 Lio s lgorithm on more omplex grph e f f G 2 f G 2 f e e 2 2 P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri
16 P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Universität Dortmun Fri 6 Universität Dortmun Universität Dortmun Lio s lgorithm with tie rek heuristi Motivtion Cost Cost 6 [ Leupers]
17 Tierek funtion Aess grph (V,E,w), for eh ege e with weight w(e): T( e) w( e ) e E, e e 6 e 4 e' e' T(e)= In se of lterntive equlweight eges: give priority to the ege with lower weight T(e), euse this will (generlly) leve more freeom for seleting further highweight eges 6 4 e e' T(e)= P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 7
18 Comprison of ifferent SOA lgorithms Overhe [%] Runtime [mses] Delrtion Orer Lio, s presente Lio, with tie rek heuristis for eges of sme weight Atri: itertive improvement of initil SOA solution Sme s Atri, with tierek heuristi e Geneti lgorithm [Leupers] Brnh & Boun (for simple ses) 0 >> P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 8
19 Vrile olesing SOA (CSOA) Exmple: Aess sequene (v,x,v,u,v,u,v,y,u,y,u,x,u,x,u,x,u) v y x u Interferene grph y v 3 Aess grph y u 4 6 v x 2 Aess grph y, v Itertive extension of Hmilton pth n olesing Memory lyout u x 7 2 u 6 x y,v u x P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 9
![Offset osts reltive to Lio [%] P. Mrweel, Univ.](/docs-images/72/67066481/images/20-0.jpg "Dortmun/Informtik 2 ICD/ES, 2006 [Desiree")
20 Offset osts reltive to Lio [%] P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 [Desiree Ottoni et l.: Improving Offset Assignment through Simultneous Vrile Colesing, SCOPES, 2003] Fri 20
![Memory size reutions [%] P. Mrweel, Univ.](/docs-images/72/67066481/images/21-0.jpg "Dortmun/Informtik 2 ICD/ES, 2006 [D.")
21 Memory size reutions [%] P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 [D. Ottoni et l.: Improving Offset Assignment through Simultneous Vrile Colesing, SCOPES, 2003] Fri 2
22 Integrte Sheuling n SOA: ShSOA Result for SOA CSOA P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 22
23 Integrte Sheuling n SOA: ShSOA Result for ShSOA [Y. Choi, T. Kim, Aress Assignment Comine with Sheuling in DSP Coe Genertion, DAC, 2002, ACM] P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 23
24 GOA: Aress ssignment for k ress registers Two ses. All esses to vrile one with the sme ress register Prtitioning of vriles into sets 2. Allotion of ress registers for eh ess to vrile. Better results, ut more omplex. A A2 A A2 P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 f j f j 2 2! Fri 24 t t
25 GOA with vrile prtitioning: Aress ssignment for k ress registers 6 See: k eges of highest weight. 4 e f Itertion: A ege(s) with smllest inrementl ost for eges not overe. Ege not overe Disjoint sets of vrs GOA k SOA [Leupers & Mrweel, ICCAD, 996] P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 2
26 Optimise use of m moifyregisters Given: Sequene of MoifyVlues: Lo AR,0 AR =2 AR =4 AR =3 AR =2 AR =3 AR =2 AR =4 AR =2 AR =4 No seprte ress lultion yle if onstnts re ontine in moify registers Moify registers re ontiners, onstnts represent ontents. Try to ssign ontents to ontiners suh tht ontentmisses our s less frequent s possile. Equivlent to pges n pge frmes. Optiml pge replement lgorithm of Bely n e pplie (reple pge with lrgest forwr istne) P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 26 [Leupers]
27 Optimising the use of m moify registers Given: sequene of moify vlues MR Lrgest forwr istne MR2 Lrgest forwr istne P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 [Leupers&Mrweel, ICCAD, 996] Fri 27
28 Integrte memory llotion/ Moify register ssignment Stnr pproh Memory llotion Simultneous Optimistion using geneti lgorithm: Perentge of sve ress omputtion yles (Sequene length,# Vriles) (00,90) (00,0) M register ssignment (00,0) (0,40) (0,20) k=m=8 k=m=4 k=m=2 (0,0) % P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 28 [Leupers, Dvi; ISSS 98]
29 Work on lrger utoinrement/erement rnges Coesize [kb] s funtion of the numer of ress registers (k) n the inrement rnges (r), ol numers inite minimum Meiumsize progrm k r Smll progrm k r (k=3, r=) n (k=2, r=3) re useful esigns. Lrger rnges o not reue oe size. Refererene: Sursnm, Lio, Devs: Anlysis n Aress Arithmeti Cpilities in Custom DSP Arhitetures, DAC, 997, p P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 29
30 (Some) Generliztions of SOA Sh SOA Lim Sh GOA Choi SOA Lio, Leupers GOA Leupers CSOA N/A Ottoni P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 30
31 Comprison of ifferent pprohes for (k,m,r)oa Author(s) Soure Prolem (k,m,r) APA OA A S M Approh Brtley Lio (,0,) ICCAD 96 (k,0,) Hmilton pth tie rek Geotys ICCAD 97 (k,0,r) Network flow Sursnm DAC 97 (k,0,r) Effet of r on oe size VLSI 97 (k,0,) Fous on rrys in loops ISSS 98 (k,m,) Geneti lgorithm Lim CODES 200 (,0,) VAG eges minimize uring sheuling Choi, Kim DAC 2002 (k,0,) Ottoni SCOPES 2003 (,0,) Vrile olesing Wess SCOPES 2004 (k,0,r) Iterte APAGOA yles k= ress regs.; m=moif. regs.; r: offset rnge; APA: ress pointer ss.; OA: offset ss.; A: ess se (), prtitione vriles (); S: integrte sheuling (); M: moulo t U. Dortm P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 3
32 Multiple memory nks Smple hrwre XMem From AGU or immeite X0 X Y0 Y Multiplier YMem From AGU or immeite Shifter ALU A B Shifter Prllel moves possile if using ifferent memory nks P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 32
33 Multiple memory nks Constrint grph genertion Preompte oe (symoli vriles n registers) Move v0,r0 v,r Move v2,r2 v3,r3 Constrint grph v0 v {XMem, YMem} r0 r {X0,X,Y0, Y, A, B} Do not ssign to sme register v2 v3 {XMem, YMem} r2 r3 {X0,X,Y0, Y, A,B} Links mintine, more onstrints... P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 33
34 Multiple memory nks Coe size reution through simulte nneling pm rv2 rv lms fir Convolution iir iqu Rel upte Complex upte Complex multiply 0 20 % 40 % 60 % [Sursnm, Mlik, 99] P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 34
35 Summry Exploiting some of the speil fetures of emee proessors in ompilers utoinrement n erement moes ress pointer ssignment prolem (APA) simple offset ssignment prolem (SOA) SOA with vrile olesing integrte sheuling generl offset ssignment prolem use of moify registers multiple memory nks P. Mrweel, Univ. Dortmun/Informtik 2 ICD/ES, 2006 Fri 3
Technology Mapping Method for Low Power Consumption and High Performance in General-Synchronous Framework
R-17 SASIMI 015 Proeeings Tehnology Mpping Metho for Low Power Consumption n High Performne in Generl-Synhronous Frmework Junki Kwguhi Yukihie Kohir Shool of Computer Siene, the University of Aizu Aizu-Wkmtsu
CS 491G Combinatorial Optimization Lecture Notes
CS 491G Comintoril Optimiztion Leture Notes Dvi Owen July 30, August 1 1 Mthings Figure 1: two possile mthings in simple grph. Definition 1 Given grph G = V, E, mthing is olletion of eges M suh tht e i,
Counting Paths Between Vertices. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs. Isomorphism of Graphs
Isomorphism of Grphs Definition The simple grphs G 1 = (V 1, E 1 ) n G = (V, E ) re isomorphi if there is ijetion (n oneto-one n onto funtion) f from V 1 to V with the property tht n re jent in G 1 if
Now we must transform the original model so we can use the new parameters. = S max. Recruits
MODEL FOR VARIABLE RECRUITMENT (ontinue) Alterntive Prmeteriztions of the pwner-reruit Moels We n write ny moel in numerous ifferent ut equivlent forms. Uner ertin irumstnes it is onvenient to work with
Mid-Term Examination - Spring 2014 Mathematical Programming with Applications to Economics Total Score: 45; Time: 3 hours
Mi-Term Exmintion - Spring 0 Mthemtil Progrmming with Applitions to Eonomis Totl Sore: 5; Time: hours. Let G = (N, E) e irete grph. Define the inegree of vertex i N s the numer of eges tht re oming into
Common intervals of genomes. Mathieu Raffinot CNRS LIAFA
Common intervls of genomes Mthieu Rffinot CNRS LIF Context: omprtive genomis. set of genomes prtilly/totlly nnotte Informtive group of genes or omins? Ex: COG tse Mny iffiulties! iology Wht re two similr
Lecture 6: Coding theory
Leture 6: Coing theory Biology 429 Crl Bergstrom Ferury 4, 2008 Soures: This leture loosely follows Cover n Thoms Chpter 5 n Yeung Chpter 3. As usul, some of the text n equtions re tken iretly from those
The DOACROSS statement
The DOACROSS sttement Is prllel loop similr to DOALL, ut it llows prouer-onsumer type of synhroniztion. Synhroniztion is llowe from lower to higher itertions sine it is ssume tht lower itertions re selete
CIT 596 Theory of Computation 1. Graphs and Digraphs
CIT 596 Theory of Computtion 1 A grph G = (V (G), E(G)) onsists of two finite sets: V (G), the vertex set of the grph, often enote y just V, whih is nonempty set of elements lle verties, n E(G), the ege
22: Union Find. CS 473u - Algorithms - Spring April 14, We want to maintain a collection of sets, under the operations of:
22: Union Fin CS 473u - Algorithms - Spring 2005 April 14, 2005 1 Union-Fin We wnt to mintin olletion of sets, uner the opertions of: 1. MkeSet(x) - rete set tht ontins the single element x. 2. Fin(x)
Algebra 2 Semester 1 Practice Final
Alger 2 Semester Prtie Finl Multiple Choie Ientify the hoie tht est ompletes the sttement or nswers the question. To whih set of numers oes the numer elong?. 2 5 integers rtionl numers irrtionl numers
CSE 332. Sorting. Data Abstractions. CSE 332: Data Abstractions. QuickSort Cutoff 1. Where We Are 2. Bounding The MAXIMUM Problem 4
Am Blnk Leture 13 Winter 2016 CSE 332 CSE 332: Dt Astrtions Sorting Dt Astrtions QuikSort Cutoff 1 Where We Are 2 For smll n, the reursion is wste. The onstnts on quik/merge sort re higher thn the ones
Implication Graphs and Logic Testing
Implition Grphs n Logi Testing Vishwni D. Agrwl Jmes J. Dnher Professor Dept. of ECE, Auurn University Auurn, AL 36849 vgrwl@eng.uurn.eu www.eng.uurn.eu/~vgrwl Joint reserh with: K. K. Dve, ATI Reserh,
Coding Techniques. Manjunatha. P. Professor Dept. of ECE. June 28, J.N.N. College of Engineering, Shimoga.
Coing Tehniques Mnjunth. P mnjup.jnne@gmil.om Professor Dept. of ECE J.N.N. College of Engineering, Shimog June 8, 3 Overview Convolutionl Enoing Mnjunth. P (JNNCE) Coing Tehniques June 8, 3 / 8 Overview
Laboratory for Foundations of Computer Science. An Unfolding Approach. University of Edinburgh. Model Checking. Javier Esparza
An Unfoling Approh to Moel Cheking Jvier Esprz Lbortory for Fountions of Computer Siene University of Einburgh Conurrent progrms Progrm: tuple P T 1 T n of finite lbelle trnsition systems T i A i S i i
Algorithm Design and Analysis
Algorithm Design nd Anlysis LECTURE 5 Supplement Greedy Algorithms Cont d Minimizing lteness Ching (NOT overed in leture) Adm Smith 9/8/10 A. Smith; sed on slides y E. Demine, C. Leiserson, S. Rskhodnikov,
Metaheuristics for the Asymmetric Hamiltonian Path Problem
Metheuristis for the Asymmetri Hmiltonin Pth Prolem João Pero PEDROSO INESC - Porto n DCC - Fule e Ciênis, Universie o Porto, Portugl jpp@f.up.pt Astrt. One of the most importnt pplitions of the Asymmetri
for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx
![for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx](/thumbs/74/70408252.jpg "for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx")
Applitions of Integrtion Are of Region Between Two Curves Ojetive: Fin the re of region etween two urves using integrtion. Fin the re of region etween interseting urves using integrtion. Desrie integrtion
Metodologie di progetto HW Technology Mapping. Last update: 19/03/09
Metodologie di progetto HW Tehnology Mpping Lst updte: 19/03/09 Tehnology Mpping 2 Tehnology Mpping Exmple: t 1 = + b; t 2 = d + e; t 3 = b + d; t 4 = t 1 t 2 + fg; t 5 = t 4 h + t 2 t 3 ; F = t 5 ; t
I 3 2 = I I 4 = 2A
ECE 210 Eletril Ciruit Anlysis University of llinois t Chigo 2.13 We re ske to use KCL to fin urrents 1 4. The key point in pplying KCL in this prolem is to strt with noe where only one of the urrents
SOLUTIONS TO ASSIGNMENT NO The given nonrecursive signal processing structure is shown as
SOLUTIONS TO ASSIGNMENT NO.1 3. The given nonreursive signl proessing struture is shown s X 1 1 2 3 4 5 Y 1 2 3 4 5 X 2 There re two ritil pths, one from X 1 to Y nd the other from X 2 to Y. The itertion
Solutions for HW9. Bipartite: put the red vertices in V 1 and the black in V 2. Not bipartite!
Solutions for HW9 Exerise 28. () Drw C 6, W 6 K 6, n K 5,3. C 6 : W 6 : K 6 : K 5,3 : () Whih of the following re iprtite? Justify your nswer. Biprtite: put the re verties in V 1 n the lk in V 2. Biprtite:
Solutions to Problem Set #1
CSE 233 Spring, 2016 Solutions to Prolem Set #1 1. The movie tse onsists of the following two reltions movie: title, iretor, tor sheule: theter, title The first reltion provies titles, iretors, n tors
Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point
GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply
Resources. Introduction: Binding. Resource Types. Resource Sharing. The type of a resource denotes its ability to perform different operations
Introduction: Binding Prt of 4-lecture introduction Scheduling Resource inding Are nd performnce estimtion Control unit synthesis This lecture covers Resources nd resource types Resource shring nd inding
Algorithm Design and Analysis
Algorithm Design nd Anlysis LECTURE 8 Mx. lteness ont d Optiml Ching Adm Smith 9/12/2008 A. Smith; sed on slides y E. Demine, C. Leiserson, S. Rskhodnikov, K. Wyne Sheduling to Minimizing Lteness Minimizing
Part 4. Integration (with Proofs)
Prt 4. Integrtion (with Proofs) 4.1 Definition Definition A prtition P of [, b] is finite set of points {x 0, x 1,..., x n } with = x 0 < x 1
Monochromatic Plane Matchings in Bicolored Point Set
CCCG 2017, Ottw, Ontrio, July 26 28, 2017 Monohromti Plne Mthings in Biolore Point Set A. Krim Au-Affsh Sujoy Bhore Pz Crmi Astrt Motivte y networks interply, we stuy the prolem of omputing monohromti
The Minimum Label Spanning Tree Problem: Illustrating the Utility of Genetic Algorithms
The Minimum Lel Spnning Tree Prolem: Illustrting the Utility of Genetic Algorithms Yupei Xiong, Univ. of Mrylnd Bruce Golden, Univ. of Mrylnd Edwrd Wsil, Americn Univ. Presented t BAE Systems Distinguished
Lecture 11 Binary Decision Diagrams (BDDs)
C 474A/57A Computer-Aie Logi Design Leture Binry Deision Digrms (BDDs) C 474/575 Susn Lyseky o 3 Boolen Logi untions Representtions untion n e represente in ierent wys ruth tle, eqution, K-mp, iruit, et
A Primer on Continuous-time Economic Dynamics
Eonomis 205A Fll 2008 K Kletzer A Primer on Continuous-time Eonomi Dnmis A Liner Differentil Eqution Sstems (i) Simplest se We egin with the simple liner first-orer ifferentil eqution The generl solution
6.5 Improper integrals
Eerpt from "Clulus" 3 AoPS In. www.rtofprolemsolving.om 6.5. IMPROPER INTEGRALS 6.5 Improper integrls As we ve seen, we use the definite integrl R f to ompute the re of the region under the grph of y =
Data Structures LECTURE 10. Huffman coding. Example. Coding: problem definition
Dt Strutures, Spring 24 L. Joskowiz Dt Strutures LEURE Humn oing Motivtion Uniquel eipherle oes Prei oes Humn oe onstrution Etensions n pplitions hpter 6.3 pp 385 392 in tetook Motivtion Suppose we wnt
Review of Gaussian Quadrature method
Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge
CS261: A Second Course in Algorithms Lecture #5: Minimum-Cost Bipartite Matching
CS261: A Seon Course in Algorithms Leture #5: Minimum-Cost Biprtite Mthing Tim Roughgren Jnury 19, 2016 1 Preliminries Figure 1: Exmple of iprtite grph. The eges {, } n {, } onstitute mthing. Lst leture
arxiv: v1 [cs.dm] 24 Jul 2017
![arxiv: v1 [cs.dm] 24 Jul 2017](/thumbs/75/71496365.jpg "arxiv: v1 [cs.dm] 24 Jul 2017")
Some lsses of grphs tht re not PCGs 1 rxiv:1707.07436v1 [s.dm] 24 Jul 2017 Pierluigi Biohi Angelo Monti Tizin Clmoneri Rossell Petreshi Computer Siene Deprtment, Spienz University of Rome, Itly pierluigi.iohi@gmil.om,
Engr354: Digital Logic Circuits
Engr354: Digitl Logi Ciruits Chpter 4: Logi Optimiztion Curtis Nelson Logi Optimiztion In hpter 4 you will lern out: Synthesis of logi funtions; Anlysis of logi iruits; Tehniques for deriving minimum-ost
Eigenvectors and Eigenvalues
MTB 050 1 ORIGIN 1 Eigenvets n Eigenvlues This wksheet esries the lger use to lulte "prinipl" "hrteristi" iretions lle Eigenvets n the "prinipl" "hrteristi" vlues lle Eigenvlues ssoite with these iretions.
XML and Databases. Outline. 1. Top-Down Evaluation of Simple Paths. 1. Top-Down Evaluation of Simple Paths. 1. Top-Down Evaluation of Simple Paths
Outline Leture Effiient XPth Evlution XML n Dtses. Top-Down Evlution of simple pths. Noe Sets only: Core XPth. Bottom-Up Evlution of Core XPth. Polynomil Time Evlution of Full XPth Sestin Mneth NICTA n
Lesson 2.1 Inductive Reasoning
Lesson 2.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 12, 16,, 2. 400, 200, 100, 50, 25,, 3. 1 8, 2 7, 1 2, 4, 5, 4. 5, 3, 2,
Graph Theory. Simple Graph G = (V, E). V={a,b,c,d,e,f,g,h,k} E={(a,b),(a,g),( a,h),(a,k),(b,c),(b,k),...,(h,k)}
Grph Theory Simple Grph G = (V, E). V ={verties}, E={eges}. h k g f e V={,,,,e,f,g,h,k} E={(,),(,g),(,h),(,k),(,),(,k),...,(h,k)} E =16. 1 Grph or Multi-Grph We llow loops n multiple eges. G = (V, E.ψ)
CS 2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2014
S 224 DIGITAL LOGI & STATE MAHINE DESIGN SPRING 214 DUE : Mrh 27, 214 HOMEWORK III READ : Relte portions of hpters VII n VIII ASSIGNMENT : There re three questions. Solve ll homework n exm prolems s shown
( ) { } [ ] { } [ ) { } ( ] { }
![( ) { } [ ] { } [ ) { } ( ] { }](/thumbs/96/129291861.jpg "( ) { } [ ] { } [ ) { } ( ] { }")
Mth 65 Prelulus Review Properties of Inequlities 1. > nd > >. > + > +. > nd > 0 > 4. > nd < 0 < Asolute Vlue, if 0, if < 0 Properties of Asolute Vlue > 0 1. < < > or
Subsequence Automata with Default Transitions
Susequene Automt with Defult Trnsitions Philip Bille, Inge Li Gørtz, n Freerik Rye Skjoljensen Tehnil University of Denmrk {phi,inge,fskj}@tu.k Astrt. Let S e string of length n with hrters from n lphet
Factorising FACTORISING.
Ftorising FACTORISING www.mthletis.om.u Ftorising FACTORISING Ftorising is the opposite of expning. It is the proess of putting expressions into rkets rther thn expning them out. In this setion you will
I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
Global alignment. Genome Rearrangements Finding preserved genes. Lecture 18
Computt onl Biology Leture 18 Genome Rerrngements Finding preserved genes We hve seen before how to rerrnge genome to obtin nother one bsed on: Reversls Knowledge of preserved bloks (or genes) Now we re
AP CALCULUS Test #6: Unit #6 Basic Integration and Applications
AP CALCULUS Test #6: Unit #6 Bsi Integrtion nd Applitions A GRAPHING CALCULATOR IS REQUIRED FOR SOME PROBLEMS OR PARTS OF PROBLEMS IN THIS PART OF THE EXAMINATION. () The ext numeril vlue of the orret
Section 2.3. Matrix Inverses
Mtri lger Mtri nverses Setion.. Mtri nverses hree si opertions on mtries, ition, multiplition, n sutrtion, re nlogues for mtries of the sme opertions for numers. n this setion we introue the mtri nlogue
MCH T 111 Handout Triangle Review Page 1 of 3
Hnout Tringle Review Pge of 3 In the stuy of sttis, it is importnt tht you e le to solve lgeri equtions n tringle prolems using trigonometry. The following is review of trigonometry sis. Right Tringle:
System Validation (IN4387) November 2, 2012, 14:00-17:00
System Vlidtion (IN4387) Novemer 2, 2012, 14:00-17:00 Importnt Notes. The exmintion omprises 5 question in 4 pges. Give omplete explntion nd do not onfine yourself to giving the finl nswer. Good luk! Exerise
Outline Data Structures and Algorithms. Data compression. Data compression. Lossy vs. Lossless. Data Compression
5-2 Dt Strutures n Algorithms Dt Compression n Huffmn s Algorithm th Fe 2003 Rjshekr Rey Outline Dt ompression Lossy n lossless Exmples Forml view Coes Definition Fixe length vs. vrile length Huffmn s
We will see what is meant by standard form very shortly
THEOREM: For fesible liner progrm in its stndrd form, the optimum vlue of the objective over its nonempty fesible region is () either unbounded or (b) is chievble t lest t one extreme point of the fesible
Separable discrete functions: recognition and sufficient conditions
Seprle isrete funtions: reognition n suffiient onitions Enre Boros Onřej Čepek Vlimir Gurvih Novemer 21, 217 rxiv:1711.6772v1 [mth.co] 17 Nov 217 Astrt A isrete funtion of n vriles is mpping g : X 1...
NON-DETERMINISTIC FSA
Tw o types of non-determinism: NON-DETERMINISTIC FS () Multiple strt-sttes; strt-sttes S Q. The lnguge L(M) ={x:x tkes M from some strt-stte to some finl-stte nd ll of x is proessed}. The string x = is
2.4 Theoretical Foundations
2 Progrmming Lnguge Syntx 2.4 Theoretil Fountions As note in the min text, snners n prsers re se on the finite utomt n pushown utomt tht form the ottom two levels of the Chomsky lnguge hierrhy. At eh level
EE 108A Lecture 2 (c) W. J. Dally and P. Levis 2
EE08A Leture 2: Comintionl Logi Design EE 08A Leture 2 () 2005-2008 W. J. Dlly n P. Levis Announements Prof. Levis will hve no offie hours on Friy, Jn 8. Ls n setions hve een ssigne - see the we pge Register
Lesson 2.1 Inductive Reasoning
Lesson 2.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 12, 16,, 2. 400, 200, 100, 50, 25,, 3. 1 8, 2 7, 1 2, 4, 5, 4. 5, 3, 2,
y = c 2 MULTIPLE CHOICE QUESTIONS (MCQ's) (Each question carries one mark) is...
. Liner Equtions in Two Vriles C h p t e r t G l n e. Generl form of liner eqution in two vriles is x + y + 0, where 0. When we onsier system of two liner equtions in two vriles, then suh equtions re lle
Vidyalankar S.E. Sem. III [CMPN] Discrete Structures Prelim Question Paper Solution
![Vidyalankar S.E. Sem. III [CMPN] Discrete Structures Prelim Question Paper Solution](/thumbs/96/126844436.jpg "Vidyalankar S.E. Sem. III [CMPN] Discrete Structures Prelim Question Paper Solution")
S.E. Sem. III [CMPN] Discrete Structures Prelim Question Pper Solution 1. () (i) Disjoint set wo sets re si to be isjoint if they hve no elements in common. Exmple : A = {0, 4, 7, 9} n B = {3, 17, 15}
Necessary and sucient conditions for some two. Abstract. Further we show that the necessary conditions for the existence of an OD(44 s 1 s 2 )
Neessry n suient onitions for some two vrile orthogonl esigns in orer 44 C. Koukouvinos, M. Mitrouli y, n Jennifer Seerry z Deite to Professor Anne Penfol Street Astrt We give new lgorithm whih llows us
Aperiodic tilings and substitutions
Aperioi tilings n sustitutions Niols Ollinger LIFO, Université Orléns Journées SDA2, Amiens June 12th, 2013 The Domino Prolem (DP) Assume we re given finite set of squre pltes of the sme size with eges
Project 6: Minigoals Towards Simplifying and Rewriting Expressions
MAT 51 Wldis Projet 6: Minigols Towrds Simplifying nd Rewriting Expressions The distriutive property nd like terms You hve proly lerned in previous lsses out dding like terms ut one prolem with the wy
On a Class of Planar Graphs with Straight-Line Grid Drawings on Linear Area
Journl of Grph Algorithms n Applitions http://jg.info/ vol. 13, no. 2, pp. 153 177 (2009) On Clss of Plnr Grphs with Stright-Line Gri Drwings on Liner Are M. Rezul Krim 1,2 M. Siur Rhmn 1 1 Deprtment of
Solutions to Chapte 7: Channel Coding
to Chpte 7: Chnnel Coing (Bernr Sklr) Note: Stte igrm, tree igrm n trellis igrm for K=3 re sme only hnges will our in the output tht epens upon the onnetion vetor. Mnjunth. P (JNNCE) Coing Tehniques July
CS 360 Exam 2 Fall 2014 Name
CS 360 Exm 2 Fll 2014 Nme 1. The lsses shown elow efine singly-linke list n stk. Write three ifferent O(n)-time versions of the reverse_print metho s speifie elow. Eh version of the metho shoul output
Preview 11/1/2017. Greedy Algorithms. Coin Change. Coin Change. Coin Change. Coin Change. Greedy algorithms. Greedy Algorithms
Preview Greed Algorithms Greed Algorithms Coin Chnge Huffmn Code Greed lgorithms end to e simple nd strightforwrd. Are often used to solve optimiztion prolems. Alws mke the choice tht looks est t the moment,
Unit 4. Combinational Circuits
Unit 4. Comintionl Ciruits Digitl Eletroni Ciruits (Ciruitos Eletrónios Digitles) E.T.S.I. Informáti Universidd de Sevill 5/10/2012 Jorge Jun 2010, 2011, 2012 You re free to opy, distriute
Chapter 2 Finite Automata
Chpter 2 Finite Automt 28 2.1 Introduction Finite utomt: first model of the notion of effective procedure. (They lso hve mny other pplictions). The concept of finite utomton cn e derived y exmining wht
B Veitch. Calculus I Study Guide
Clculus I Stuy Guie This stuy guie is in no wy exhustive. As stte in clss, ny type of question from clss, quizzes, exms, n homeworks re fir gme. There s no informtion here bout the wor problems. 1. Some
Computing all-terminal reliability of stochastic networks with Binary Decision Diagrams
Computing ll-terminl reliility of stohsti networks with Binry Deision Digrms Gry Hry 1, Corinne Luet 1, n Nikolos Limnios 2 1 LRIA, FRE 2733, 5 rue u Moulin Neuf 80000 AMIENS emil:(orinne.luet, gry.hry)@u-pirie.fr
A Lower Bound for the Length of a Partial Transversal in a Latin Square, Revised Version
A Lower Bound for the Length of Prtil Trnsversl in Ltin Squre, Revised Version Pooy Htmi nd Peter W. Shor Deprtment of Mthemtil Sienes, Shrif University of Tehnology, P.O.Bo 11365-9415, Tehrn, Irn Deprtment
1 This diagram represents the energy change that occurs when a d electron in a transition metal ion is excited by visible light.
1 This igrm represents the energy hnge tht ours when eletron in trnsition metl ion is exite y visile light. Give the eqution tht reltes the energy hnge ΔE to the Plnk onstnt, h, n the frequeny, v, of the
Genetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary
Outline Genetic Progrmming Evolutionry strtegies Genetic progrmming Summry Bsed on the mteril provided y Professor Michel Negnevitsky Evolutionry Strtegies An pproch simulting nturl evolution ws proposed
Fast Frequent Free Tree Mining in Graph Databases
The Chinese University of Hong Kong Fst Frequent Free Tree Mining in Grph Dtses Peixing Zho Jeffrey Xu Yu The Chinese University of Hong Kong Decemer 18 th, 2006 ICDM Workshop MCD06 Synopsis Introduction
Surds and Indices. Surds and Indices. Curriculum Ready ACMNA: 233,
Surs n Inies Surs n Inies Curriulum Rey ACMNA:, 6 www.mthletis.om Surs SURDS & & Inies INDICES Inies n surs re very losely relte. A numer uner (squre root sign) is lle sur if the squre root n t e simplifie.
6. Suppose lim = constant> 0. Which of the following does not hold?
CSE 0-00 Nme Test 00 points UTA Stuent ID # Multiple Choie Write your nswer to the LEFT of eh prolem 5 points eh The k lrgest numers in file of n numers n e foun using Θ(k) memory in Θ(n lg k) time using
Nondeterminism and Nodeterministic Automata
Nondeterminism nd Nodeterministic Automt 61 Nondeterminism nd Nondeterministic Automt The computtionl mchine models tht we lerned in the clss re deterministic in the sense tht the next move is uniquely
CS415 Compilers. Lexical Analysis and. These slides are based on slides copyrighted by Keith Cooper, Ken Kennedy & Linda Torczon at Rice University
CS415 Compilers Lexicl Anlysis nd These slides re sed on slides copyrighted y Keith Cooper, Ken Kennedy & Lind Torczon t Rice University First Progrmming Project Instruction Scheduling Project hs een posted
MATH 122, Final Exam
MATH, Finl Exm Winter Nme: Setion: You must show ll of your work on the exm pper, legily n in etil, to reeive reit. A formul sheet is tthe.. (7 pts eh) Evlute the following integrls. () 3x + x x Solution.
Section 1.3 Triangles
Se 1.3 Tringles 21 Setion 1.3 Tringles LELING TRINGLE The line segments tht form tringle re lled the sides of the tringle. Eh pir of sides forms n ngle, lled n interior ngle, nd eh tringle hs three interior
Chapter 4 State-Space Planning
Leture slides for Automted Plnning: Theory nd Prtie Chpter 4 Stte-Spe Plnning Dn S. Nu CMSC 722, AI Plnning University of Mrylnd, Spring 2008 1 Motivtion Nerly ll plnning proedures re serh proedures Different
Solids of Revolution
Solis of Revolution Solis of revolution re rete tking n re n revolving it roun n is of rottion. There re two methos to etermine the volume of the soli of revolution: the isk metho n the shell metho. Disk
Solutions to Assignment 1
MTHE 237 Fll 2015 Solutions to Assignment 1 Problem 1 Find the order of the differentil eqution: t d3 y dt 3 +t2 y = os(t. Is the differentil eqution liner? Is the eqution homogeneous? b Repet the bove
Welcome. Balanced search trees. Balanced Search Trees. Inge Li Gørtz
Welome nge Li Gørt. everse tehing n isussion of exerises: 02110 nge Li Gørt 3 tehing ssistnts 8.00-9.15 Group work 9.15-9.45 isussions of your solutions in lss 10.00-11.15 Leture 11.15-11.45 Work on exerises
Area and Perimeter. Area and Perimeter. Solutions. Curriculum Ready.
Are n Perimeter Are n Perimeter Solutions Curriulum Rey www.mthletis.om How oes it work? Solutions Are n Perimeter Pge questions Are using unit squres Are = whole squres Are = 6 whole squres = units =
THE EXISTENCE-UNIQUENESS THEOREM FOR FIRST-ORDER DIFFERENTIAL EQUATIONS.
THE EXISTENCE-UNIQUENESS THEOREM FOR FIRST-ORDER DIFFERENTIAL EQUATIONS RADON ROSBOROUGH https://intuitiveexplntionscom/picrd-lindelof-theorem/ This document is proof of the existence-uniqueness theorem
CSC2542 State-Space Planning
CSC2542 Stte-Spe Plnning Sheil MIlrith Deprtment of Computer Siene University of Toronto Fll 2010 1 Aknowlegements Some the slies use in this ourse re moifitions of Dn Nu s leture slies for the textook
Efficient Parameterized Algorithms for Data Packing
Effiient Prmeterized Algorithms for Dt Pking Krishnendu Chtterjee, Amir Kfshdr Gohrshdy, Nstrn Okti, Andres Pvloginnis To ite this version: Krishnendu Chtterjee, Amir Kfshdr Gohrshdy, Nstrn Okti, Andres
Precise timing analysis for direct-mapped caches
Preise timing nlysis for diret-mpped hes Sidhrt Andlm, Roopk Sinh, Prth Roop, Alin Girult, Jn Reineke To ite this version: Sidhrt Andlm, Roopk Sinh, Prth Roop, Alin Girult, Jn Reineke. Preise timing nlysis
Generalization of 2-Corner Frequency Source Models Used in SMSIM
Generliztion o 2-Corner Frequeny Soure Models Used in SMSIM Dvid M. Boore 26 Mrh 213, orreted Figure 1 nd 2 legends on 5 April 213, dditionl smll orretions on 29 My 213 Mny o the soure spetr models ville
A Transformation Based Algorithm for Reversible Logic Synthesis
2.1 A Trnsformtion Bsed Algorithm for Reversile Logi Synthesis D. Mihel Miller Dept. of Computer Siene University of Vitori Vitori BC V8W 3P6 Cnd mmiller@sr.uvi. Dmitri Mslov Fulty of Computer Siene University
Towards Efficient Consistency Enforcement for Global Constraints in Weighted Constraint Satisfaction
Towrs Effiient Consisteny Enforement for Glol Constrints in Weighte Constrint Stisftion J. H. M. Lee n K. L. Leung Deprtment of Computer Siene n Engineering The Chinese University of Hong Kong, Shtin,
Ranking Generalized Fuzzy Numbers using centroid of centroids
Interntionl Journl of Fuzzy Logi Systems (IJFLS) Vol. No. July ning Generlize Fuzzy Numers using entroi of entrois S.Suresh u Y.L.P. Thorni N.vi Shnr Dept. of pplie Mthemtis GIS GITM University Vishptnm
University of Sioux Falls. MAT204/205 Calculus I/II
University of Sioux Flls MAT204/205 Clulus I/II Conepts ddressed: Clulus Textook: Thoms Clulus, 11 th ed., Weir, Hss, Giordno 1. Use stndrd differentition nd integrtion tehniques. Differentition tehniques
ILLUSTRATING THE EXTENSION OF A SPECIAL PROPERTY OF CUBIC POLYNOMIALS TO NTH DEGREE POLYNOMIALS
ILLUSTRATING THE EXTENSION OF A SPECIAL PROPERTY OF CUBIC POLYNOMIALS TO NTH DEGREE POLYNOMIALS Dvid Miller West Virgini University P.O. BOX 6310 30 Armstrong Hll Morgntown, WV 6506 millerd@mth.wvu.edu
Situation Calculus. Situation Calculus Building Blocks. Sheila McIlraith, CSC384, University of Toronto, Winter Situations Fluents Actions
Plnning gent: single gent or multi-gent Stte: complete or Incomplete (logicl/probbilistic) stte of the worl n/or gent s stte of knowlege ctions: worl-ltering n/or knowlege-ltering (e.g. sensing) eterministic
March eq Implementing Additional Reasoning into an Efficient Look-Ahead SAT Solver
Mrh eq Implementing Additionl Resoning into n Effiient Look-Ahed SAT Solver Mrijn Heule, Mrk Dufour, Joris vn Zwieten nd Hns vn Mren Deprtment of Informtion Systems nd Algorithms, Fulty of Eletril Engineering,
Sections 5.3: Antiderivatives and the Fundamental Theorem of Calculus Theory:
Setions 5.3: Antierivtives n the Funmentl Theorem of Clulus Theory: Definition. Assume tht y = f(x) is ontinuous funtion on n intervl I. We ll funtion F (x), x I, to be n ntierivtive of f(x) if F (x) =
Let s divide up the interval [ ab, ] into n subintervals with the same length, so we have
![Let s divide up the interval [ ab, ] into n subintervals with the same length, so we have](/thumbs/79/79376941.jpg "Let s divide up the interval [ ab, ] into n subintervals with the same length, so we have")
III. INTEGRATION Eonomists seem muh more intereste in mrginl effets n ifferentition thn in integrtion. Integrtion is importnt for fining the epete vlue n vrine of rnom vriles, whih is use in eonometris