正規描述與自動驗證 Formal Description & Automated Verification 王 凡 國立台灣大學 電機 程系
Verification （驗證） ? l l 找出系統設計中的所有錯誤。 確認系統中已經（接近）沒有錯誤。 非常困難！ 複雜系統的決勝關鍵！ 各位同學的一條生路！ 台灣產業的一條生路！
簡介 l 瞭解電腦系統的 formal semantics l 學習電腦輔助驗證的理論與製作
當然愛你啦！北鼻 你愛不愛人家嗎 ！ ？ 你曾經對我說，永遠愛著我！ …? ? …!! 如果你媽 和我一起 掉下水，你 要先救誰 厚！ ？ 以後 、房 存款 的名 子是 下？ 誰
瞭解電腦系統的 formal semantics divide (a, b) { while (a > 0) a = a-b; if (a == 0) return 1; else return 0; } Is this program correct ? do I know How It what it is a is checks if supposed to divisible by b. do ? I doubt it! What happens Well, when b = 0 ? sometimes happens!
瞭解電腦系統的 formal semantics divide (a, b) { while (a > 0) a = a-b; if (a == 0) return 1; else return 0; } Seriously, what does “a=a-b; ” means ? What does this `if’ statement means ?
瞭解電腦系統的 formal semantics l l When we say a program is correct, what is the behavior model of the program ? What is the mathematics of program behaviors ?
瞭解電腦系統的 formal semantics state, possible world (②, 10, 3) ① divide (a, b) { (③, 10, 3) a=a-b; ② while (a > 0) (②, -2, 3) (②, 7, 3) ¬a>0 a=a-b; ③ a = a-b; Kripke structure (④, -2, 3) ④ if (a == 0) return 1; (③, 1, 3) ¬a==0 (③, 7, 3) a=a-b; (⑤, -2, 3) a>0 ⑤ else return 0; (②, 4, 3) (②, 1, 3) ⑥} a>0 a=a-b; (③, 4, 3)
瞭解電腦系統的 formal semantics - an attempt ic! et ithm at state k; p(k): theer ar an statement ① divide (a, b) { ord value c at at state k; a(k): the ools of st- f t r ② while (a > 0) Fib(k): t the value dic at state k; o preof b lo ou A y ors. ③ a = a-b; lp havi am he be gr ④ if (a == 0) returnhe e pro t 1; h of t ⑤ else return 0; ⑥} k 0(p(k)== ③ a(k+1)==a(k)-b(k))
太棒了！北鼻！ 兩位好瞎！一 有了 logics，我們 定沒有修過離 The wonderful logics! 現在可以清楚瞭 散、邏輯。 解彼此的行為與 Goedel已經證 結構。 明有些定理是 邏輯無法判別 的。 ！一 倫倫 切的誤會， 即使可以判 都可以說 別，但也可 清楚，講 能有 state明白了。 space爆炸問 題呀！
Some incomputable problems (1/2) The validity of 1 st-order logic formula (Hilbert’s 2 nd problem) x y z(single(x) (parent(y, x) worried(y)) l Mortal matrix problem Given 15 3 3 matrices, M 1, …, M 15, are there Mi 1 … Mim = 0 ? l CFL ambiguity problem l 12 -11
Some incomputable problems (2/2) l Multivariable polynomial equations (Hilbert’s 10 th problem) Incomputable for degree 4. Incomputable for 36 real variables. Incomputable for 11 integer variables. 12 -12
學習電腦輔助驗證的理論與製 作 Goedel’s incompleteness theorem: l 任何有限規則系統，都有一個無法證明的事實。 State-space explosion problem ? l l When a and b are both 32 bits long, # states 232 The safety analysis problem of Boolean program is PSPACEcomplete. The satisfiability problem of LTL is PSPACE-complete. The satisfiability problem of 1 st-order logics is undecidable! – l No algorithm exists! The safety analysis problem of algorithm is undecidable!
Things to learn in the course l State-transition models of computer systems – l l l Only with mathematical models, you can build EDA tools. Mathematical model construction Verification algorithms Practical techniques to overcome the complexity!
Things to learn in the course State-transition models of computer systems l Kripke structures
Things to learn in the course Mathematical model construction l With REDLIB packages l for automata with dense-time clocks
Things to learn in the course Verification algorithms l BDD manipulation algorithm for propositional logics l Automata (regular expression) learning l Linear temporal logic satisfiability checking l Automata safety and liveneness analysis l CTL model checking l Automata simulation checking
Things to learn in the course Practical techniques to overcome the complexity! l BDD-based techniques
Course plan： l Basic understanding of the knowledge of computer verification l Three projects – – – use REDLIB to solve board games use REDLIB to construct system model and making verification for untimed systems use REDLIB to do model-based testing for timed systems
Course schedule Introduction （教師請假，待補課） Propositoinal Logic & BDD technology 1 st project announcement 10/5 Propositoinal Logic & BDD technology 10/12 State Machines & Learning 10/19 State Machines 10/26 State Machines 1 st project report, 2 nd project announcement 11/2 State Machines 1. 9/14 2. 9/21 3. 9/28 4. 5. 6. 7. 8.
Course schedule (continued) 9. 10. 12. 13. 11/9 11/16 11/23 11/30 Temporal Logics & Symbolic Model-Checking Midterm Exam Temporal Logics & Symbolic Model-Checking 2 nd project report, 3 rd project announcement. 14. 12/7 Embedded Systems 15. 12/14 Simulation & Bisimulation 15. 12/21 Game theories 16. 12/28 Model-based Testing 17. 1/4 3 rd project report 18. 1/11 Final exam 9 am-11: 50 am
課程網頁 http: //cc. ee. ntu. edu. tw/~farn/courses/FMV/ 助教： 何宗諭 travisho 0014@gmail. com Tuesday p. m. 2: 00~3: 00, 明達館 631
Evaluation Two scenarios Without paper presentation midterm: 30%, final: 30%, projects: 30%, homework: 10%
參考資料： l l l Handbook of Logic in Computer Science: Vol. 1 -2, edited by S. Abramsky (1993), Oxford. Handbook of Theoretical Computer Science, Vol. A & B, edited by J. van Leeuwen, Elsevier. Model Checking, E. Clarke, O. Grumberg, D. Peled, MIT Press Formal Methods for Real-Time Systems edited by C. Heitmeyer, D. Mandrioli, Wiley 重要論文
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