??????????? –

1
?????????? ????????????????? ? ??????????

• ?. ???????
• ?. ????????

2
????

• ????? ???????
• ??????
• ??????
• ??????????? ? ??????????

3
???????????

• ???????????
• ???????? ????????????
• ??????????? ??????????
• ????? ?????????? ??
• ????????? ? ???????????,
• ???????????????? ??
• ?????????? ??????
• ?????????

??????????
????????? ???????
(????????? ???????)'
???????
4
?????????? ???????????

• ?????????? ????????
• ?????? ???? ???????????? ? ???? ??????????
  ???????
• ??????????
• ??????????
• ???????????? ????? ???? ?????? ???? ??????????
  ?????????

?????????? I
???????????? S
5
?????????? ? ????????????

• ????????? ????? ????????? ?????? ???-??
  ??????????
• ???????? ??????????? ? ???????? ???????
  ???????????
• ????????? ???????????? ????? ?????????? ???????
  ????? ??????? ?????????

????????????
??????????
???????
6
?????? ???????????

• ??????????? ? ?????????? ???????????
• ?????????? ???????????
• ???????????
• ????? ?????????? E. F. Moore 1956
• ??????
• ?? Floyd 1967, Hoare 1969
• ????????
• ? ???????? ?? 19791995
• ?????? ???
• ????? ??????? ????????? ????? ??????????
  ?????????
• ????????? ?????? ??????????? ????
• ???????? ???????????? ?????? ????????? ??????????
• ???????? ???????? ? ??????? ???????????? ? ??????
  ?????????

7
????? ??????????

• ???????? ??????? ?????????? ??????
• ???? ????????? ??????? ???????????

• ??????????? ?????? ???? ?????????????
• ??????????? ?????? ???? ?????????

8
?????????? ? ?????????

• ?????????? ???????? ??????
• ?? ????????? ?????? ?????????? ???????
  ???????????
• ???? ??????????
• ??????????? ??????????
• ?????????????? ??????????
• ?????????? ??????
• ?????????? ??????????????
• ????????? ??????????

9
????

• ????? ???????
• ??????
• ??????
• ??????????? ? ??????????

10
???????? ???? ???????

• ???? ???????????
• ??????-?????????????? L
• ???????????? (??????????) E
• ???? ????????????
• ??????????? I ? S (I ? S) L - L
• ????????????? I ? S E - L
• ????????? I ? S E - E

11
??????-??????????????

• ??????????????
• ??????????? ??????? (Codd - 1970)
• ??????????? ???? ?????? (Zilles, Liskov 1974)
• ??????? ?????????
• CSP (Hoare - 1978)
• CCS (Milner - 1980)
• ACP (Bergstra, Klop - 1982)
• Abstract State Machines (??????? - 1984)
• ??????????

12
??????????
µ-?????????? (Pratt, Kozen 1982)
µ, ?
?????????
ITL (Moszkowski 1983)
CTL (Clarke, Emerson - 1981)
A, E
TPTL (Alur, Henzinger - 1989)
????? ?????
G, F, X, U
LTL (Prior - 1957)
? ?? ????????
Hoare logic (Hoare - 1969)
? ? ?? ????????
?-?????????? (Church 1936)
????
?????? 1-?? ???????
? ?? ?????
?????????? ????????????
?-?????????? ??????? ??????? (Girard 1971)
?????? ?????? ???????? (Peirce 1885)
? ? ?? ??????????/?????
13
????????????
?-???????? (Buchi 1960)
ASM
????????? (Alur, Henzinger - 1996)
?-?????
????????? (Alur, Dill - 1990)
Statecharts (Harel 1987)
???????
???? ????? (Petri 1962)
?????????? I/O
LTS (1980 ?) ??????? ?????????
??????????????
IOA (Tuttle, Lynch 1987)
??????
FSM (Huffman -1954)
?????? (??????? 1936)
EFSM (1973 ?)
CFSM (Brand, Zafiropulo - 1983)
14
????

• ????? ???????
• ??????
• ??????
• ??????????? ? ??????????

15
?????? ???????????

• ? ?????? ??????????????
• ???????????? ? ?????????? ????????
• ? ???????? ??????????????
• ???????? ?????? ????????????

S
I
?
???????
S
I
?
16
?????? ?????????????

• ??????????? ?????? (theorem proving) Floyd
  1967
• ???????? ??????? (model checking) Clarke,
  Emerson 1981
• ???????? ????????? (simulation checking,
  equivalence checking) Moore 1956
• ????????????? ?????????? (symbolic execution)
  Topor, Burstall 1972
• ??????????? ????????????? (abstract
  interpretation) Cousot 1975

17
???????? ?????????????

• ?????????? ???????????? (formal conformance
  testing) ??????????? 1973Hennessy, DeNicola
  1984
• ??????????????? ?????????? (runtime
  verification, passive testing) ? 1970-? ????
  ????? ?????, ? ??????? ???? ?????? ??
  ???????????? 1999 ?????? (Havelund, Rosu ?)
  

18
????????????? ?????
Theorem proving
Provers, SAT solvers
Abstract interpretation
Model checkingModel checkers
Symbolic execution
Simulation checking
Formal conformance testing
Runtime verification
19
????

• ????? ???????
• ??????
• ??????
• ??????????? ? ??????????

20
??????????? ??????

• ???????????????????? ??????
• ASM
• ?????????????????? ??????
• ACL2 (Boyer, J. S. Moore 1971) 20 ????????,
  JVM (700 ???????)
• HOL (Gordon, 1988) 30 ????????
• PVS (Owre, Rushby, Shankar 1992) 30 ????????
• Isabelle
• Coq

21
???????? ??????? ? ?????????

• Model checkers
• SPIN (Holzman 1982)
• SMV (McMillan et al. 1994) ? ???????????
• Murf (Dill 1992)
• UPPAAL (Larsen et al. 1995)
• Equivalence checkers
• Verity (Kuehlmann et al. 1995)
• ?????????
• CADP (INRIA 1990) 50 ???????? ??????????

22
??? ?????????

• ????????????
• TGV (1997)
• Gotcha (1999)
• ??????????
• TemporalRover (1995)
• ESC/Java 2 (2002)
• Java PathFinder (2004)
• Abstract interpretation
• ASTREE (2001)

23
??????? ?? ????????!
24
??????????? ?????? I

• ???????????????????? ?????? ASM
• ?????? ?????????????? ??????? Java
• (??? ?????????? ? ??.)
• ???????, Schulte, Wallace 1999
• ????????? JVM, Java ? ??????????????
• (??? ????????????)
• Borger, Schimd, Stark 2001
• ????????? SDL 2000
• Eschbach, Glasser, Gotzhein, Prinz 2000

25
??????????? ?????? II

• R. S. Boyer, J. S. Moore
• ???????????? ?????? 1-?? ??????? Applicative
  Common Lisp
• 1971 ?????? ??????????
• 1986 Nqthm
• 2001 ACL2
• ?????? ??????????
• ??????????
• FM8501, FM8502 (1985) FM9001 (1997)
• Motorola MC68020 (1993), CAP DSP (100 ???????)
• AMD K5 (1995), Athlon (1997)
• IBM 4758 security model
• Rockwell
• JVM (2001-2004) (700 ???????)

26
??????????? ?????? III

• HOL (Gordon 1988)
• ??????? ?? LCF (Milner 1973) higher-order
  logic ML
• ????????? ???????? ????? ?? ?????????? HOL
• ????? ?????? (1996)
• ??????????
• TAMARACK (1987)
• Viper (1987)
• Intel (Harrison, OLeary)
• ??
• Web-?????? (1995)
• ?????????

?????? ???????????????? ???????????? ?????????
????? ??????????? ??????? ??????!
27
??????????? ?????? IV

• PVS (Owre, Rushby, Shankar 1992)
• higher-order logic ????, ??????? ?? VDM
• ???? ????????? ???????? ??????????
• ?????????
• ???????? ?????? (NASA) (1996-1998)
• ????? ???? ?? (1998)
• ??????????? ??????? ??? (1999)
• ??????????
• AAMP5 (1995)
• VAMP FPU (2005)