Black Box Checking.

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Black Box Checking Book: Part 9 Model Checking Limited state depiction of a framework B . LTL equation . Make an interpretation of  into a machine P . Check whether L( B )  L( P )=. Provided that this is true, S fulfills . Something else, the crossing point incorporates a counterexample. Rehash for various properties.
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Discovery Checking Book: Chapter 9

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Model Checking Finite state depiction of a framework B . LTL recipe . Make an interpretation of  into a machine P . Check whether L( B )  L( P )=. Provided that this is true, S fulfills . Something else, the crossing point incorporates a counterexample. Rehash for distinctive properties.  

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Buchi automata ( w - automata) S - limited arrangement of states. ( B has l  n states) S 0  S - introductory states. ( P has m states) S - limited letters in order. (contains p letters) d  S ï‚\' S ï‚\' S - move connection. F  S - tolerating states. Tolerating run: passes a state in F interminably regularly. Framework automata: F=S , deterministic.

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Example: check  an a <>  a  a  an, a

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a  an a  an Example: check <>  a  <>  a

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Example: check <> a  an, a <>  ~ a  a  a Use programmed interpretation calculations, e.g., [Gerth,Peled,Vardi,Wolper 95]

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a c b System

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Every component in the item is a counter sample for the checked property. an a s 1 s 2 q 1  a b c a  a q 2 s 3 a s 1 ,q 1 s 2 ,q 1 Acceptance is dictated via machine P . b a s 1 ,q 2 s 3 ,q 2 c

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 Testing Unknown deterministic limited state framework B . Known: n states and letter set . A theoretical model C of B . C fulfills every one of the properties we need from B . Check conformance of B and C . Another form: just a bound n on the quantity of states l is known.

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Given Finite state framework B . Move connection of B known. Property speak to via machine P . Check if L( B )  L( P )=  . Chart hypothesis or BDD systems. Intricacy: polynomial. Obscure Finite state framework B . Letters in order and number of conditions of B or upper bound known. Detail given as a theoretical framework C. Check if B  C . Unpredictability: polynomial if number states known. Exponential generally. Model Checking/Testing

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Property speak to via robot P . Check if L( B )  L( P )=  . Diagram hypothesis methods. Obscure Finite state framework B . Letters in order and Upper bound on Number of conditions of B known. Multifaceted nature: exponential. Discovery checking  

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Combination lock robot Accepts just words with a particular addition ( cdab in the illustration). c d a b s 1 s 2 s 3 s 4 s 5

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 b an a b a b a  a b Conformance testing Cannot recognize if decreased or not.

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a b a Conformance testing (cont.) When the black box is nondeterministic, we may never test a few decisions.

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a Conformance testing (cont.)  b an a  a b an a b Need: bound on number of conditions of B .

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Need dependable RESET a b s 1 s 2 an a s 3

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Vasilevskii calculation Known machine A has l states. Discovery machine has up to n states. Check every move. Watch that there are no "combination lock" slips. Many-sided quality: O(l 2 n p n-l+1 ). At the point when n=l : O(l 3 p).

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reset an a b c attempt c attempt b an a b c an a b c b c come up short Experiments

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Simpler issue: gridlock? Nondeterministic calculation: figure a way of length  n from the introductory state to a halt state. Straight time, logarithmic space. Deterministic calculation: methodicallly attempt ways of length  n , in a steady progression (and utilization reset ), until stop is come to. Exponential time, direct space.

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Deadlock unpredictability Nondeterministic calculation: Linear time, logarithmic space. Deterministic calculation: Exponential ( p n-1 ) time, direct space. Lower bound: Exponential time (use mix lock automata). How can this acclimate with what we think about multifaceted nature hypothesis?

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Modeling discovery checking Cannot model utilizing Turing machines: not all the data about B is given. Just sure analyses are permitted. We take in the model as we make the investigations. Can utilize the model of recreations of deficient data .

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Games of deficient data Two players: $-player,  - player (here, deterministic). Limitedly numerous arrangements C. Counting: Initial C i , Winning : W + and W - . An equality connection @ on C (the $-player can\'t recognize proportional states). Names L on moves (attempt a , reset , achievement , come up short ). The $-player has the moves marked the same from setups that are comparable. Technique for the $-player: will prompt a setup in W +  W - . Can\'t recognize identical conf. Nondet. procedure : closes with W + . Can recognize.

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Modeling BBC as diversions Each arrangement contains a machine and its present state (and that\'s only the tip of the iceberg). Moves of the $-player are marked with attempt a , reset ... Moves of the  - player with achievement , fall flat . c 1 @ c 2 when the automata in c 1 and c 2 would react in the same route to the investigations in this way.

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An innocent method for BBC Learn first the dark\'s structure box. At that point apply the crossing point. Specify automata with  n states (without rehashing isomorphic automata). For a current automata and new automata , develop a recognizing arrangement. One and only of them survives. Unpredictability: O(( n+1 ) p ( n+1 )/n !)

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On-the-fly procedure Systematically (as in the gridlock case), discover two arrangements v 1 and v 2 of length <= m n . Applying v 1 to P conveys us to a state t that is tolerating. Applying v 2 to P takes us back to t . Apply v 1 (v 2 ) n+1 to B . On the off chance that this succeeds, there is a cycle in the crossing point marked with v 2 , with t as the P (tolerating) part. Many-sided quality: O ( n 2 p 2mn m ).

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Learning a robot Use Angluin’s calculation for taking in a machine. The learning calculation questions whether a few strings are in the robot B . It can likewise guess a machine M i and requests a counterexample. It then produces a robot with more states M i+1 et cetera.

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A technique taking into account learning Start the learning calculation. Inquiries are just investigations to B . For a guessed robot M i , check if M i  P =  If along these lines, we check conformance of M i with B (Vasilevskii calculation). In the event that nonempty, it contains some v 1 (v 2 ) w . We test B with v 1 (v 2 ) n+1 . On the off chance that this succeeds: blunder, generally, this is a counterexample for M i .

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Black Box Checking Strategy Incremental learning inconsistency false negative Model Path Model Checking no counterexample discovery testing Comparing counterexample System real blunder conformance built up Report lapse No mistake discovered

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Complexity l - genuine size of B . n - an upper bound of size of B . p - size of letter set. Lower bound: reachability is like stop. O(l 3 p l + l 2 mn) if there is a blunder. O(l 3 p l + l 2 n p n-l+1 + l 2 mn) if there is no lapse. On the off chance that n is not known, check while time permits.

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Some investigations Basic framework written in SML (by Alex Groce, CMU). Try different things with discovery utilizing Unix I/O. Permits sans model checking of C code with between procedure correspondence. Incorporating tried code in SML with BBC program as one procedure.

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Conclusions Black box checking is a mix of testing and model checking. On the off chance that a tight bound on size of B is given: learn B to begin with, then do model checking. Tight lower b

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