kỹ thuật bmc (bounded model checking)

kỹ thuật bmc (bounded model checking)

 MỤC LỤC BẢNG KÝ HIỆU        Directed Acyclic Graph   !!" !!" !#" !#" $ $ %" %&" # Boolean Satisfiability #' #' !()*+ Lớp : 10BĐTVT- KH  PHẦN I: GIỚI THIỆU 1.1. Model Checking ,-./0123, 435460789:.;<24;; =>1?@(6=AB0C-38#4D4 .E,42FG@E6HI,-.( F?600C8 ,=>6=>J1@BK4KLM1 /=>6=>2NOE:@/0F1P,.E8!; 1QR2/4S1J414PT-(U@4 9FV2-4G@2/,-.6=AV Q8-=W@,-.6=AVQ,46O6, GK0OR=A(8,-.@2B6NFP, .E@?3N2B6N>,=>6=>2/G6F P(/BK4KLM016N,06OF/6O F/0QP6O6,8,-..;X2Y -14V@KZK0O-KZK0@2/S46HF [AP6OF-84/Q>K9P,- .K\0-.1@K,]6OF@2/,.[A P6OF816=A-.(=4?6014J12/ BT@/-5=4?60@-(4I32/ 6=A4CV?,;2/(J14/436N- ,^8 !()*_ Lớp : 10BĐTVT- KH  1.2. BDDs và BMC 1.2.1. BBD (Binary Decision Diagram) /K,6\ (=D-Q/ K,]0/ 80T6=A42D0K;2/((168 01K,]4H6TPK;+8`144Ha8 b16PT/cd2/4T4P8 9eT6=Ad Kf1-/ag2/T6=AdKf10/+g8!Dh =D/@1KV4,34H+PK;2/1KV96163 4Ha8!T/-(12/(44T/-6=Ad2/ 6=AX/  P80T4OT5@K,3KM0. 2-@-6=A4K;2/T-6i6=A6OKM4HaO+8j0 DP6=AK,3KMkk/i5T8j,644 0/6=A613Kf02D4HP46Q2/=DP(@ 9KZ6QRT52/6416,l46=W7 6=AS46HKf44HK;80T6=AO@31KV9O 46=A?3-m96=AS46HKf4HK;PT8 )FG@1TS@196=ASn;;SB4Ha@=A1.14 6=ASn;8!;6=W766;T5a@./6=A6442Na8!; 6=W66;T5+./6=A6442N4H+8 1.2.2. BMC (Bounded Model Checking) -.,D1@S^?0K,E LC2/d35,;14>K9(, 0<J1P?,;14/61D414h ^318-.?V4PG#-9@6(23 .;-"#P#c(,>D<LCK0 6;72/-(-/m8 ,E36,P,-.D1 /35,;@o/K,EW2//D1 =W[B Quan hệ chuyển tiếp là [ ] ( ) ( ) 0 1 : , 1 0 k k M I s T s s i i i −   = ∧   + = ∧ !()*p Lớp : 10BĐTVT- KH  1.3. Ưu điểm của BMC ,-.@6O6,6=AK,]W 2/356=A-.(=0414J18)DJ ;;?;@514P35(,B02/?P -14fV-,?36=A8,-.=A =2DC(P414J1@(,6N,>+a 148@01FZPK,E@=W6=Ae G=?K,K]>K9PK0,-.=A=80, -.?V=W(9:6N,352D/: K;148V@2D4-.D>45? ,-.fVh4D9:F4318VJ@? XE?RKV9P4K;/BhX8#?./ P0E?K;/;h9L=W5WO Q?3KM8)DN2FG@-\1-E?K; 3G8 4PGh;6H36N#m160V4K,E =-eG41FZ8T-H9=f R?K[i-D1P2/(,6N,42B6NL C36N2D/.K;8#?V6=A4G/ -NN4=,QE@=>E@ ,.EP4356N,6=W@2/435h 1*805h4.?3h9/9G842FG64,/ -Gq'$)r?V=>4#2/#$?VPG2 sq8 D30,-.=A=?VPG #8t=f/SnK06;7PN/V2/40K,E 36N/LCoo=0K0K06;7\18-=W@D 343P,-.D1@>D1/N/56 P0K06;78BM,-.D1W ;F(,6=A9D?LC36NK,EW 8j,EF6T6Z2//2YP@;064 EJ,-.352/,-.(8-5 J4;=DD,-.@=>4-VQ S^?19O;KH?608 !()*u Lớp : 10BĐTVT- KH  #?3AFP-3=vjQV@,-.3 5.;K06;7B8jN//N^K6QVP 4PG.;#8!=WM.;4K06;7/6OF hXBP,-.8E@(.;4K06;7 N/5,8jOF/T=W[,K06;76> 9>8EK@,-.D1eGF->? V4385[@-5?V43@, -.D1-Q0E?K;6=A?XKMOZ S;1W5608#?L64^O6H=W/6Q 6P8 j444I;@/30-G?V,- .D18j=42FG6(#?V,-.(I w5>?V,-.805=WA, -.D143<E@414K 6Q(,-6=A18 Ví dụ xn4146>9K\0HpK2D4K VI,Syaz@Sy+z@2/Sy_z80FS@S{I,h3,; J44HS312/44H14S{;2/=>6=> 2Dv 14K6Q0PS(,[X80 F*SI3414K6Q/8 b.+8f0h3,;_Q2/Ki2`O H/6=A4<B94KF;KMap V;8!=D30<h3,;4 !()*| Lớp : 10BĐTVT- KH  H14;PSy_z@>04H-6T+6=AeG ;a86(@6OF/5[c<2;S}a05K=D 6Q6P/-6T8jOF/(,6=A4K,K,E "S}a8H2B6N,-.iK;"2/2B6N, -.\1KfP6HK,E8#6(@,;(0<? 3// 8.;2D06=WKB~@D14 6=W(•+14@M1X}_8 Xp146QVP 6=WS a @S + @2/S _ 2/BS a /14K6QS.+80GK 6QPS(,KB~@-(KBED1PSa8fh3 6i    Q  2/      K,  E  3  6N  o  6=A  6H  w  = ( ) ( ) ( ) 0 0 1 1 2 , ,I x T x x T x x ∧ ∧ 8f06HwP2/*@2/(K,E v [ ] [ ] ( ) [ ] [ ] ( ) [ ] ( ) 1 0 1 0 0 0 1 1 2 2 1x x x x x = ∧ = ∧ = ∧ K=D6QV [ ] [ ] ( ) [ ] [ ] ( ) [ ] ( ) 2 1 2 1 2 0 1 1 2 2 1x x x x x = ∧ = ∧ = K=DE B~6=W/2Dp14/E? ( ) 0G x ≠  9K \02`O86(@VQM(0?,6iRS _ 2N14 K6Q@D14E@ODF(mSf.+8K, ]?,6i/6=A6Hw=S _ @S + /=>6=>2D K,Ev [ ] [ ] ( ) [ ] [ ] ( ) [ ] ( ) 2 2 0 1 1 2 2 1 i i i x x x x x = ∧ = ∧ = 5[@9ZZM6=W/c?34/K0 D1KfK,E ( ) 0G x ≠ 8=WA/@6OF#6Hw = 0 i x ≠ 96=AJ1<148#=>6=>2DK,E [ ] ( ) [ ] ( ) [ ] ( ) 0 1 1 1 2 1 i i i x x x = ∧ = ∧ = !()*€ Lớp : 10BĐTVT- KH  jO4/2/[B9@K,E36N 2 0 2 0 M i i i f V L S i = = ∧ ∧ ∧ + ,E/LC2/d(0K06;7PN/_ K,E5"S}a82FG@.;0n4LC K,E+KM4; [ ] : 1 i x j = B9@•}a@+@_ PHẦN II: ĐẶC ĐIỂM CỦA KỸ THUẬT BMC 6=A6Hw=0P4K,EP/ 1P6H-=W2/K\d4K0=Ae(6=Wi K;80K,E/1P6H-=W!!";?P6Hd SB3=D436NQe8r6=A6Hw[04@ =d4K0=Ae6=W\16=An8Sn4e=A; x@4e;h9"@4ei, 2/4eD‚89;M 4K,E/!!"8(,-K;6i0K,E!!"/ !()*ƒ Lớp : 10BĐTVT- KH  -Q:F=D\4eZ' ( ) ( ) R i Uf g ff f g ¬ ¬ ¬ 80 K,E-(K0=Ae7rO6=An8K/K4 /@2/,-.8(,6=Af06,6N ,X2Y„8 Định nghĩa 1. 0BT/0A ( ) , , ,M S I T = l 2D0 K014J1#@A414K6Q  I S ⊆ @5h3 ,  6i  J  4  1  4  T S S ⊆ × @  2/  C  P  4  1  4 ( ) : S P A → l 2D36NQe eG4BT=4-.6,6=44K, 8dSn4BT/(C(8VQM { } 0,1 n S = @2/<146((,6=AK,]Kf02P4K; 14 ( ) ( ) ( ) 1 , ,s s s n = 2D@}+@…@/4K;36N8 6Hw4K,E36N ( ) I f s @ ( ) , T f s t  2/ ( ) p f s   ( ) ( ) ( ) ( ) ( ) iff s I, , , , à s I I p f s f s t iff s t T v f s iff s ∈ ∈ ∈ l 8j,  6> 9  e G @ ( ) , T f s t …VJ@VQMX14(01 4;;8)DXQe  s S ∈  (0Qe  t S ∈  2D  ( ) ,s t T ∈ 8)D ( ) ,s t T ∈ m2; s t → 8)D0<4142-1 ( ) 0 1 , , s s π = @ !()*† Lớp : 10BĐTVT- KH  6Hw ( ) i i s π = 2/ ( ) 1 , , i i i s s voii IN π + = ∈ 80<142-1/ 06=W; ( ) ( ) 1i i π π → + 2DX i IN ∈ Định nghĩa 2 (phát biểu) 9e/0BT@ π /6=WP2/o/0K,E 8#6(‡k}oo/6TV π 6=A6Hw=v Định nghĩa 3 F[A 0K,Eo///6T0BT 4I3k}ooo‡k}oB946=W π 2D ( ) 0 I π ∈ 80K,E o/\16T0BT4I3k}Eo; \106=W π 2D‡k}o2/ ( ) 0 I π ∈ x46H0K,E/\16TBT=D 6=AX/0K//,-.\18 ?=>FD44K,P„@],M0K,E o///6TBToo ¬ o-9\16T8 j,9h;K/4,-.iK;@94K,E2/B MK/4,-.\1K,E6=AP6H-(9 48M?4e.;0K06;7@2/;-/ -.K,E///6T86(@dSSnK/4,- .\18 !()*ˆ Lớp : 10BĐTVT- KH  t=f>K9P,-.D1/dSSn/6QD 1P6=W/(,/0942DK/4,-.\18 D1N/P/6QKfD1/6(8?;: QD1@.;4K06;7/>(,8 O[/6QP6=W/J1@(27(,K,]06=W 2-1;(02`O=AR145[P/6QDKB ~14/=D6(._K8!;-(2`O=A._@. /6Q-(KBE.2N142-1P6=W8)FG@d0/ 6Q2D02`O=A(,K,]KME 8O[J VB9414R a D  @=-(2`O=AR  D 14=D6(@V-,;T@9.0KME -,J1 •+ 8 b._8b=WAPK=DD1 Định nghĩa 4.  )D‰X06=W‡02`@;‡Š‡2/ u v ω π = × 2D ( ) ( ) ( ) 0 , , 1u l π π = ⇔ 2/ ( ) ( ) ( ) , ,v l k π π = 8X‡6>902`; (0 l IN ∈ 2D l k ≤ ‡/02`@8 04K,D1/0nSBSdD4K,-D 1P6Hw_8!(n6HwK/4,-.D 12/G;c0?,6iPK/4,- .D1/K/4?36=A8 44K,D1dSn/6QJ1P06=W8 -=W@deG414•+6QV  a @…@   P0 6=W6,S46H4HPK,EV6=W6(8!;06=W/0 !()*+a Lớp : 10BĐTVT- KH [...]... với các kỹ thuật suy giảm không gian trạng thái đưa ra bài toán thú vị khác Bảng 2 Bộ dịch Barrel (|r|= số thanh ghi, sec là giây, MB= Mega Bytes) Nhóm VI 23 Lớp : 10BĐTVT- KH Kỹ thuật BMC( Bounded Model Checking) Bảng 3 Bảng 4 Bộ đếm mẫu cho Nhóm VI 24 Lớp : 10BĐTVT- KH Kỹ thuật BMC( Bounded Model Checking) TÀI LIỆU THAM KHẢO 1 Armin Biere, Alessandro Cimatti, Edmund Clarke, Yunshan Zhu, Symbolic Model. .. ( ‘-g5’) và giá trị rất lớn (‘-g50’) Chú ý rằng bít tràn phụ thuộc vào tất cả các bit của bộ nhân tuần tự và xuất hiện trong đặc tính kỹ thuật Vì vậy, nón của sự suy giảm ảnh hưởng không thể xóa bỏ bất cứ cái gì Nhóm VI 21 Lớp : 10BĐTVT- KH Kỹ thuật BMC( Bounded Model Checking) Bảng 1 Dịch tuần tự 16*16 bit và bổ sung bộ nhân với cờ tràn và 16 bits đầu ra Trong cột SMV1 của bảng 1, bản chính thức của... Kích thước của  thức con thông thường được chia sẻ ( như trong công cụ BMC) Nó là bậc hai trong k và tuyến tính trong kích thước của các biểu thức mệnh đề cho T, I và p ∈ A Do đó, kiểm tra mô hình giới hạn tồn tại có thể suy giảm trong thời gian mệnh đề tới sự thực hiện mệnh đề Nhóm VI 13 Lớp : 10BĐTVT- KH Kỹ thuật BMC( Bounded Model Checking) Để xây dựng [ M , f ]    k , đầu tiên ta định nghĩa biểu... kém chặt chẽ hơn CTL* (2) Hoặc LTL hoặc CTL bao hàm cái còn lại Hình 3 : Mối quan hệ của CTL*, CTL và LTL Nhóm VI 20 Lớp : 10BĐTVT- KH Kỹ thuật BMC( Bounded Model Checking) PHẦN III:KẾT QUẢ & HƯỚNG NGHIÊN CỨU TIẾP THEO 3.1 Kết quả Ta đã hoàn thiện một bộ kiểm tra mô hình BMC dựa trên kiểm tra mô hình giới hạn Ngôn ngữ đầu vào của nó là một tập con của ngôn ngữ SMV Đầu ra là một chương trình SMV hoặc biểu... một phép tuyển được bổ sung để chắc chắn rằng p giữ trên π ( j ⇔ l) đường từ π(i) tới toán tử thời gian khác Nhóm VI Nguyên nhân tương tự dẫn tới sự tịnh tiến của các 14 Lớp : 10BĐTVT- KH Kỹ thuật BMC( Bounded Model Checking)  [ g ] Sự tính tiến l   k ánh xạ một biểu thức LTL vào trong một biểu thức mệnh i đề Thông số k là chiều dài mào đầu của đường mà ta xét và i là vị trí hiện tại trong mào đầu... succ(i) ≔ i+1 với i . P80T4OT5@K,3KM0. 2-@-6=A4K;2/T-6i6=A6OKM4HaO+8j0 DP6=AK,3KMkk/i5T8j,644 0/6=A613Kf02D4HP46Q2/=DP(@ 9KZ6QRT52/6416,l46=W7 6=AS46HKf44HK;80T6=AO@31KV9O 46=A?3-m96=AS46HKf4HK;PT8 )FG@1TS@196=ASn;;SB4Ha@=A1.14 6=ASn;8!;6=W766;T5a@./6=A6442Na8!; 6=W66;T5+./6=A6442N4H+8 1.2.2. BMC (Bounded Model Checking) -.,D1@S^?0K,E LC2/d35,;14>K9(, 0<J1P?,;14/61D414h ^318-.?V4PG#-9@6(23 .;-"#P#c(,>D<LCK0 6;72/-(-/m8 ,E36,P,-.D1 /35,;@o/K,EW2//D1 =W[B Quan. ∧ ∧ + ,E/LC2/d(0K06;7PN/_ K,E5"S}a82FG@.;0n4LC K,E+KM4; [ ] : 1 i x j = B9@•}a@+@_ PHẦN II: ĐẶC ĐIỂM CỦA KỸ THUẬT BMC 6=A6Hw=0P4K,EP/ 1P6H-=W2/Kd4K0=Ae(6=Wi K;80K,E/1P6H-=W!!";?P6Hd SB3=D436NQe8r6=A6Hw[04@ =d4K0=Ae6=W16=An8Sn4e=A; x@4e;h9"@4ei,. !()*+ Lớp : 10BĐTVT- KH  PHẦN I: GIỚI THIỆU 1.1. Model Checking ,-./0123, 435460789:.;<24;; =>1?@(6=AB0C-38#4D4 .E,42FG@E6HI,-.( F?600C8 ,=>6=>J1@BK4KLM1 /=>6=>2NOE:@/0F1P,.E8!; 1QR2/4S1J414PT-(U@4 9FV2-4G@2/,-.6=AV Q8-=W@,-.6=AVQ,46O6, GK0OR=A(8,-.@2B6NFP, .E@?3N2B6N>,=>6=>2/G6F P(/BK4KLM016N,06OF/6O F/0QP6O6,8,-..;X2Y -14V@KZK0O-KZK0@2/S46HF [AP6OF-84/Q>K9P,- .K0-.1@K,]6OF@2/,.[A P6OF816=A-.(=4?6014J12/ BT@/-5=4?60@-(4I32/ 6=A4CV?,;2/(J14/436N- ,^8 !()*_