XX:8 Program Tailoring:Slicing by Sequential Criteria TD BU BU Entry Node ......ncw.cw,w){ncw} 33) ncw .cwcw w.......... …{w}…{ncw】 ncw )--(ncw.cw.w) 34 new Driver new Driver 38 dw《ncw) n 2 new() new Filewiter 2 n {Gw…Gww} 35 dconfig0☐ getSystemFale 3w)(ncw) {cw…{cww} c 27 outclose() …w}《nCw {w}…{w}… 3 getConfiglngetSystemlnlo40 {w}w …《W}…{ncw} ao902- …《w}…{nCww) Non-SC Statame fw.wrRe(12 w -Inter-prooedural control fiow End Node☐ Figure 5 A simplified GIcFG of the program given in Figure 2 for illustrating the bottom-up (BU)and top-down(TD)passes of SCDFA with SC={n→c→w,n'→c→w} BU computes a global property,PANTI,for every node n in GICFc,backwards against the control flow,starting at EXIT.PANTIout(n)represents the set of suffixes of some sequences in SCw that are partially anticipable at the entry of n,i.e.,appear on some outgoing path of n ending at EXIT.In our example,PANTIout (ENTRY)={ncw,cw,w}.As ncw is partially anticipable(but n'cw is not)at ENTRY,GICFG contains some paths passing through ncw. TD computes a global property,PAVAlL,for every node n in GICFG,forwards along the control flow,starting from ENTRY.PAVAlLi(n)specifies the set of suffixes of some sequences in PANTIot(ENTRY)to represent implicitly (for efficiency reasons)the fact that their corresponding prefixes are partially available at the entry of n,i.e.,appear on some incoming paths of n starting from ENTRY.For example,PAVAlLi(12)={ncw,w},indicating that the prefixes e and nc of ncw are partially available at the entry of node 12. For this example,a node n is included in the tailored program if PAVAlLin(n)nPANTIout(n) since a suffix s E PAVAlLin(n)nPANTIout (n)is partially anticipable at the entry of n and some sequence in SC with s removed is partially available at the entry of n.In our example,the tailored program consists of all the lines except lines 38-40. Context Sensitivity Figure 6 illustrates as an example how the TD pass shown in Figure 5 is performed for FileWriter()context-sensitively by solving a CFL-reachability-based balanced-parentheses problem,efficiently call-o-start edge.（ in the IFDS framework.For technical new Filewriter(2 details,we refer to 38.There are four 士 data-flow facts,ncw,cw,w,and 0 (for NTER FleWrer.cnnib the empty set).There are two call sites to FileWriter()at lines 2 and 2',which are identified as nodes n and n',respectively, to-return cda with their call-to-start and exit-to-return ●1 35 d.config0 edges labeled as(n:)n,(n and )n appro- ● priately.ENTER and EXIT are the start Figure 6 Context-sensitivity via CFL-reachability. and exit nodes of FileWriter(),whose CFG is irrelevant and thus elided.In SCDFA,the call-to-return edge always serves as a kill edge(to stop the data-flow facts from bypassing a callee).For each node n,PAVAlLin(n)is the set of facts,i.e.,suffixes of ncw shown in black dots.According to Figure 5,PAVAlLin(2)=PAVAlLin(2')={ncw).If FileWriter()XX:8 Program Tailoring: Slicing by Sequential Criteria TD BU BU TD 36 getConfigInfo() new Driver() 38 33 if (...) getSystemFile() 39 getSystemInfo() 40 End Node 34 new Driver(...) Entry Node 35 d.config() fw.write() 12 2 new FileWriter() new FileWriter() 2' 27 out.close() d.log() 42 { } w { } w { } w { } w { } w { } w { } w { } w { } w { } w { } cw { } cw { } ncw { } ncw { } ncw { } ncw, cw, w { } ncw, cw, w { } ncw, cw, w Non-SC Statement Inter-procedural control flow SC Statement Intra-procedural control flow { } ncw { } ncw { } ncw { } ncw { } ncw { } ncw, w { } cw, w { } cw, w n n' c w Figure 5 A simplified GICFG of the program given in Figure 2 for illustrating the bottom-up (BU) and top-down (TD) passes of SCDFA with SC w = {n→c→w, n0→c→w}. BU computes a global property, PANTI, for every node n in GICFG, backwards against the control flow, starting at EXIT. PANTIout(n) represents the set of suffixes of some sequences in SC w that are partially anticipable at the entry of n, i.e., appear on some outgoing path of n ending at EXIT. In our example, PANTIout(ENTRY) = {ncw, cw, w}. As ncw is partially anticipable (but n 0 cw is not) at ENTRY, GICFG contains some paths passing through ncw. TD computes a global property, PAVAIL, for every node n in GICFG, forwards along the control flow, starting from ENTRY. PAVAILin(n) specifies the set of suffixes of some sequences in PANTIout(ENTRY) to represent implicitly (for efficiency reasons) the fact that their corresponding prefixes are partially available at the entry of n, i.e., appear on some incoming paths of n starting from ENTRY. For example, PAVAILin(12) = {ncw, w}, indicating that the prefixes  and nc of ncw are partially available at the entry of node 12. For this example, a node n is included in the tailored program if PAVAILin(n)∩PANTIout(n) 6= ∅, since a suffix s ∈ PAVAILin(n) ∩ PANTIout(n) is partially anticipable at the entry of n and some sequence in SC w with s removed is partially available at the entry of n. In our example, the tailored program consists of all the lines except lines 38 – 40. Context Sensitivity Figure 6 illustrates as an example how the TD pass shown in Figure 5 is performed for FileWriter() context-sensitively by solving a CFL-reachability-based ( n ( n' ) n' ) n 35 d.config() getSystemFile() 39 2 new FileWriter() new FileWriter() 2' FileWriter.<init> ENTER 0 ncw cw w FileWriter.<init> EXIT 0 ncw cw w 0 ncw cw w 0 ncw cw w 0 ncw cw w 0 ncw cw w call-to-return edge call-to-start edge exit-to-return edge … … n n' Figure 6 Context-sensitivity via CFL-reachability. balanced-parentheses problem, efficiently in the IFDS framework. For technical details, we refer to [38]. There are four data-flow facts, ncw, cw, w, and 0 (for the empty set). There are two call sites to FileWriter() at lines 2 and 2 0 , which are identified as nodes n and n 0 , respectively, with their call-to-start and exit-to-return edges labeled as (n, )n, (n0 and )n0 appro￾priately. ENTER and EXIT are the start and exit nodes of FileWriter(), whose CFG is irrelevant and thus elided. In SCDFA, the call-to-return edge always serves as a kill edge (to stop the data-flow facts from bypassing a callee). For each node n, PAVAILin(n) is the set of facts, i.e., suffixes of ncw shown in black dots. According to Figure 5, PAVAILin(2) = PAVAILin(20 ) = {ncw}. If FileWriter()