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USC Computer Science Technical Reports, no. 809 (2003)
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USC Computer Science Technical Reports, no. 809 (2003)
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Æ ! "### $%&’’ ( ’)* +,* Æ ! " # $% & & ! ’ ! () * + ,’ - + ’ ! ’ + ! + ... /01)) (1 * (2* +(3* ... /01)) 4 ’ )56 7 #.8 $% 7 ! 7 1 2 .8 $ 3 7 ... /01)) 5 9 7 ) (5 * : ... /01)) ; < ! ’ ; < ! 8 ; < ! (9 * # % ! ! 8 ;. # ; . %(=* ;. ’ ;. ’ & 7 & 8 ;. #> 8 $% # % # % : ’ ! (/* > 8 $ (?* + : > 8 $ 8 # % ’ ’ $ ’ 0 G = { G 0 = {1}, G 1 = {0} } 1 > )@ @ 1 ! ! + + 8 #)% #1% #2% #3% > ) 1 ) 0 + : : ’ @ - ./ 0 : > ! ; #& % 1 1 t 0 t 1 =t 0 +d t 2 =t 0 +α r t 3 =t 0 +d+α r RTS 0,1 -TS RTS 0,1 -RS RTS 0,1 -RE RTS 0,1 -TE Event: Timeline State of Node 0: State of Node 1: Tx Idle Tx Wai t Idle Wait Rx R x Description of events: RTS-TS=RequestToSend-Transmission-Start, RTS-RS=RequestToSend-Reception-Start, RTS-TE=RequestToSend-Transmission-End, RTS-RE=RequestToSend-Reception-End. Description of states: Tx: Transmitting, Rx: Receiving Event History: RTS 0,1 -TS@t 0 , RTS 0,1 -RS@t 1 , RTS 0,1 -RS@t 2 , RTS 0,1 -RE@t 3 State History: 0: { <Idle, _, t 0 >, <Tx, t 0 , t 2 >, <Wait, t 2 , _> }, 1: { <Idle, _, t 1 >, <Rx, t 1 , t 3 >, <Wait, t 3 , _> } Time relations: 1. t 1 =t 0 +d 2. t 2 =t 0 +α r 3. t 3 =t 0 +d+ α r > 1@ @ ; #; % ; . #; .% A B ; ; #; ;% A B ; ; . #; ;.% A B B < ; > 1 ; % ; < ! ’ 2 2 2 2 # 2 2# @ ; # %( 0 * ; ;# %($ * ; .# %( 0 * ; ;.# %($ * C % " ; ) ; " 2 0 ’ C ) 2 % @ #)% #1% ! #2% + ’ % " @ + ’ . ’ @ ) # %( * 1 # %( * @ ) B 1 B ) : 1 : + ’ ! ’ > ! @ 0@ ! )@ ! @ #)% #1% ’ > 2 @ #)% #1% + ’ 3 ) @ 4 5 @ 6 > 3 3 > ! 4 @ 2 Æ Æ Æ )@ Transition Table F Topology G state, event Implication Algorithms A Search Algorithms B, P T Scenarios O Output Search Tree consistency state, event, state, event, time relation time relation Error Scenario E > 2@ D .8 $ B A m C A n D B p C q n m p m q n > 3@ States: node 0: , , <D, t 2 ,unknown>, node 1: , <C, t 1 , t 3 >, <D, t 3 , unknown >, Events: m 0,1 @ t 0 , n 0,1 @ t 1 , p 0,1 @ t 2 , q 1,0 @ t 2 Time relations: 1. t 1 = t 0 + δ 1 2. t 2 = t 0 + δ 2 3. t 3 = t 1 + δ 3 A fully specified Scenario, R 0 : States: node 0: <D, t 2 , unknown > node 1: <C, t 1 , t 3 > Events: n 0,1 @ t 1 Time relations: 1. t 3 = t 1 + δ 3 A partially specified Scenario, R 1 : Underlined entities are unjustified in the scenario > 5@ > ’ ’ @ Æ ! 2 > = 3 2 E 0 0 5 0 5 > > 3 5 @ #)% 4 #1% 6 @ ’ ’ 5 ’ 2 ’ @ 3 R 1 : States: node 0: <D, t 2 , unknown > node 1: <C, t 1 , t 3 > Events: n 0,1 @ t 1 Time relations: 1. t 3 = t 1 + δ 3 States: node 0: <D, t 2 , unknown > node 1: <C, t 1 , t 3 >, Events: n 0,1 @ t 1 Time relations: 1. t 3 = t 1 + δ 3 R 1 : > 9@ ’ ’ ’ ’ > 5 ! ’ ’ ’ ! & + ’ " . & ! ! ! > 9 ’ ; > > 3 & ! 8 211 # + ’ R 1 : States: node 0: <D, t 2 , unknown > node 1: <C, t 1 , t 3 >, Events: n 0,1 @ t 1 Time relations: 1. t 3 = t 1 + δ 3 States: node 0: <D, t 2 , unknown >, node 1: <C, t 1 , t 3 >, Events: n 0,1 @ t 1 , p 0,1 @ t 2 , m 0,1 @ t 0 Time relations: 1. t 3 = t 1 + δ 3 2. t 0 = t 1 -δ 1 States: node 0: <D, t 2 , unknown >, <C, t 1 , t 2 > node 1: <C, t 1 , t 3 >, Events: n 0,1 @ t 1 , q 0,1 @ t 2 , m 0,1 @ t 0 Time relations: 1. t 3 = t 1 + δ 3 2. t 0 = t 1 -δ 1 R 2 : > =@ + ’ 8 ’ > = ; 5 ’ 5 ; D % # 4 5 ’ % % 6 # 6 5 ’ % ! $ + 4 & + % &$ ; #;% # % #;.% # .% C 5 ’ & # .% # % . ; ;. % ( ! ! Æ Æ + ! 7 Æ + > ’! ! # Æ % > ! 7 Æ ! ! 7 Æ Æ ) ’ ’ ’ ’ * $ # "# + 1 1 + , # $ ! > ! t 0 t 1 S 1 t 2 t 3 S 2 t 0 t 1 S 1 t 2 t 3 S 2 OR Node is in both state S 1 and S 2 during period [t 2 ,t 1 ] ! Node is in both state S 2 and S 1 during period [t 0 ,t 3 ] ! Inconsistent: t 0 t 1 S 1 t 2 t 3 S 2 t 0 t 1 S 1 t 2 t 3 S 2 OR Consistent: > /@ ; ! !@ #)% #1% #2% A ! ! - $ A > / # % # % .# # % ’ <& . ’ .# ! @ > ? > / $ # % ’ 0 $ ’ 1 $ 9 V B L PQ entity x entity x entity x R flag if x is consistent set of entities that flag if x is justified in all possible entity x all possible choices from R set of entities that A entity x justifies x in all possible ways flag if x is justified in R justifies x in all possible ways ways in R > ?@ . $ ) 5 + = 8 $ > 8 ’ > 8 9 9 + 9 2 ’ ’ 8 > " # $ 3 F > ’ ’ & ’ > ’ ’ ’ 3 8 & & ! # =% # + ! ! + ! ! D = Direction of data transmission: 01 2 3 Topology II Topology III 0 13 24 Topology IV 35 0 12 4 6 7 > )0@ + % &#’ ()* ... /01)) (1 * ’ E> #E > % E> #<% . : ; #C G% ’ )0 3 + % ’ ’ ’ #E>% ; ’ ! ; < C % #+ % + ’ ; C G ! 8 ; < C G ; < E C G E E ) #> )0% 1 2 ’ E E E . E E; E E;. E ! ;! ; + + + ; + +> + > % ’ " < ; < E Æ > 1@ ’ 2 @ ) 1 2 & & HCE8 H ( * . ) @ ) # @ 1 ’ # @ E ; E ;. E ; E ;. 2 4 @ > 2 & A B #2% A B #3% ## % # %% #5% , % ’ > )) / Æ Æ 2@ > )1 )2 ’ #;% # % # )% #;.% #;% # 1% > )) ) E E C ’ ’ E E ’ > )1 E E ’ @ #)% +> . #1% 0 +> #2% 0 ! 0 +> ! ’ E ’ ’ ! > )2 . D ’ ’ ! +> . +> . +> 0 1 ! !" # $ $% % &’ % ($ # )( ( # " # ( $% $ # # )* H e : Data 0,1 -RS@t 0 , Data 0,1 -RE@t 1 , Data 2,3 -RS@τ 0 , Data 0,1 -RE@τ 1 SOI: (1) t 1 =t 0 +β (2) τ 1 =τ 0 +β (3) (t 0 ≤τ 0 , τ 0 <t 1 ) or (τ 0 ≤t 0 , t 0 <τ 1 ) Root T 0 : H e : Data 0,1 -RS@t 0 , Data 0,1 -RE@t 1 , Data 2,3 -RS@τ 0 , Data 0,1 -RE@τ 1 , Data 0,1 -TS@t 2 , Data 2,3 -TS@τ 2 SOI: (1) t 1 =t 0 +β (2) τ 1 =τ 0 +β (3) (t 0 ≤τ 0 , τ 0 <t 1 ) or (τ 0 ≤t 0 , t 0 <τ 1 ) (4) t 2 =t 0 -d (5) τ 2 =τ 0 -d T 0 : Rule 1: Data-RS Data-TS > ))@ Data i,j -TS(0)[i], Data- RS(d)[G i ], Data i,j -TE(β)[G i ], Data i,j -RE(d+β)[G i ] Tx i SIFST-E i WSIFS-C i Data 0,1 -TS @ t 2 is justified by following entities (Z y1 ): (1) Event SIFST-E 0 @ t 2 (2) State of node 0: <Tx, t 2 , unknown> (3) State of node 0: <WSIFS-C, unknown, t 2 > Comment: node 0 changes its state from WSIFS-C to Tx at time t 2 Data 2,3 -TS @ τ 2 is justified by following entities (Z y2 ): (1) Event SIFST-E 0 @ τ 2 (2) State of node 2: <Tx, τ 2 , unknown> (3) State of node 2: <WSIFS-C, unknown, τ 2 > Comment: node 0 changes its state from WSIFS-C to Tx at time τ 2 Cross product (Z y1 x Z y2 ): 2 time relations: (1) t 0 ≤τ 0 and τ 0 <t 1 (2) τ 0 ≤t 0 and t 0 <τ 1 > )1@ ’ ? H e : Data 0,1 -RS@t 0 , Data 0,1 -RE@t 1 , Data 2,3 -RS@τ 0 , Data 0,1 -RE@τ 1 , Data 0,1 -TS@t 2 , Data 2,3 -TS@ τ 2 , SIFST-E 0 @t 2 , SIFST-E 2 @ τ 2 H s : 0:<WSIFS-C, _, t 2 >, 0:<Tx, t 2 ,_>, 2:<WSIFS-C, _, τ 2 >, 2:<Tx, τ 2 ,_> SOI: (1) t 1 =t 0 +β (2) τ 1 =τ 0 +β (3) t 2 =t 0 -d (4) τ 2 =τ 0 -d (5) t 0 ≤τ 0 (6) τ 0 <t 1 H e : Data 0,1 -RS@t 0 , Data 0,1 -RE@t 1 , Data 2,3 -RS@τ 0 , Data 0,1 -RE@τ 1 , Data 0,1 -TS@t 2 , Data 2,3 -TS@ τ 2 , SIFST-E 0 @t 2 , SIFST-E 2 @ τ 2 H s : 0:<WSIFS-C, _, t 2 >, 0:<Tx, t 2 ,_>, 2:<WSIFS-C, _, τ 2 >, 2:<Tx, τ 2 ,_> SOI: (1) t 1 =t 0 +β (2) τ 1 =τ 0 +β (3) t 2 =t 0 -d (4) τ 2 =τ 0 -d (5) τ 0 ≤t 0 (6) t 0 <τ 1 Underlined entities are unjustified in tree node T 1 : H e : Data 0,1 -RS@t 0 , Data 0,1 -RE@t 1 , Data 2,3 -RS@τ 0 , Data 0,1 -RE@τ 1 , Data 0,1 -TS@t 2 , Data 2,3 -TS@τ 2 SOI: (1) t 1 =t 0 +β (2) τ 1 =τ 0 +β (3) (t 0 ≤τ 0 , τ 0 <t 1 ) or (τ 0 ≤t 0 , t 0 <τ 1 ) (4) t 2 =t 0 -d (5) τ 2 =τ 0 -d T 0 : > )2@ $ + 7 I I ... /01)) + ’ I I 1 ()0 * > ’ )0 3 ’ @ ) 3@ (E * 1 ; ;. E ; 2 #9% #=% + 8 @ ) 0 + 1 ; ; 2 C 3 ; E ( * ; 1 + 1 7 & # G% + .8 $ 1 + D; Æ 90 D .8 $ > ! G ) 2 5 = 0 1 3 9 & @ ) 0 2 1 5 3 = 9 & > )3 )5 .8 $ + 7 .8 $ 2=6 506 # 956/06 % 106306 > 56396 )56 .8 $ 7 : $ # G ) 0 1 ; 1 ; 3 ; C 3 ; 3 # % ; 9 C ; ; < ! )0 Througput: EOTG vs. Random scenarios 0 10 20 30 40 50 60 70 80 90 5 8 10 12 20 100 No. of nodes Throughput, % Random EOTG > )3@ : > ’ ! & 5 6 + E E ; ; < ! C + 3 ; + E #+E% E 3 E +E ! ; < ! F +E ! E ! E 3 ; ; ! +E 5 3 F ; +E ! ; + &# + ! $ + 7 Throughput: EOTG vs. Random scnerarios 0 10 20 30 40 50 60 70 4 9 16 25 100 No of nodes Througput % Random EOTG > )5@ ... /01)) 4 396 + ’ # % # % + ,"## -# . "/-%# ’$0 "%- (%& 1 %%1$$,* 2 ( ’ 2’* #’" # ’-%# .)* 345* 67 4*++ 388 #* 9 ,: 6) (% --$$ :(# ;#" %- %#, * <%"* 272 38* = ,: > :% --$$ "## -# ;#" "$$ 26$, ?* (%"0(% . % * "$ * ( " % 2* @(%0* A:: 38=* B ,C- #; ( "%$ # ( ";#"%- #; 4*++ : "## -#,* <( ’"%% <%(# D% 1 %$’%%* 26 384* E , ";#"%- . %’%# #; $"&’ -##"%# ;’-# ;#" 4*++ )"$$ 26 "## -# "$ - #; #& % ( "%$, <( ’"%% <%(# ’% "%* :A 388* 5 * ! 1 % * $" F ’%# &%$ 33 $0 %$ ’1> :’-%$ #’0 "## -#, :A384* 4 , %’#" $ "%# ;#" :’-%$ #’0 "## -# $0, ! 1 $" ’%* A 7? 384* 8 F1$%- $0 #; :’-%$ #’0 "## -#$> %1$$ #; #") %" % %- ) %" %"- ( - (’$ * ! 1 * $" * ’% "# -0$ #; 6 3* + ( 6 ) #" ’%#" $* ( >77)))*$*’7$%7$7*( * ))
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Shamim Begum, Sandeep Gupta, Ahmed Helmy. "Error oriented test generation for wireless AdHoc MAC protocols." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 809 (2003).
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Begum, Shamim
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Gupta, Sandeep
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Helmy, Ahmed
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USC Computer Science Technical Reports, no. 809 (2003)
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Error oriented test generation for wireless AdHoc MAC protocols (
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Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA
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Archive of computer science technical reports published by the USC Department of Computer Science from 1991 - 2017.
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USC Viterbi School of Engineering Department of Computer Science
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Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA
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In copyright - Non-commercial use permitted (https://rightsstatements.org/vocab/InC-NC/1.0/