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Hybrid Approach to Model-Checking of Timed Automata DAT4 Project Proposal Supervisor: Alexandre David

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What is Model-Checking? Idea: You define a model in a given formalism/language (TA). You give specifications in the form of formulas in a given logic (TCTL). … in a tool (UPPAAL). You press a button and: Yes, properties are satisfied (and why). No, properties are not satisfied (and why).

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What is UPPAAL? Tool developed between Uppsala University and Aalborg University. Model-checker for Timed Automata. It has a graphical interface to draw the TA = state machines with clock constraints.

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UPPAAL The GUI (java): Editor. Simulator. Verifier. The server (C++): Verification engine (model-checker).

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Timed Automata in a Nutshell! Lamp User Off LowHigh push! push? Closed system controller environment x>5 x<=5 x=0

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TA in UPPAAL Templates to define processes. Parameters. States have invariants (progress). Access to integer variables and C-like functions and syntax.

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So What’s The Problem? Model-checking here: Enumerate all the possible states = State-space exploration (enumerative!). But… size of the state-space = # of locations in every process * # of possible values for every variable * # of different (not included) zones. And that’s not good! Known as state-space explosion.

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Zones Symbolic representation of clock constraints = difference bound matrices (DBMs). Size = (clocks+1) 2, # of zones?

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Example Size of the state-space is approximately 4*4*4*4*4 (=2 10 ) * 2 (1 binary variable) * # of zones for 5 clocks (DBM 6x6) in this model ~ 4 possible values/clock to simplify = 2 10 = 2 21 states! Memory: 5+1+36 integers per state = 168 bytes -> 336MB. Add 1 process: *4*4…

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Don’t Panic! All the states are not reachable! Synchronizations and conditions between processes. The system implements some logic, it does not generate everything… but we still have the explosion.

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What’s The Project? Big fat state-space Initial state Goal state Find a path But how? Breadth first search.

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Project Idea Help the search by pruning the state- space! Cheap backward reachability with an over-approximation. Use the result to prune the search forward!

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The Idea! Big fat state-space Initial state Goal state Pruned!

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Hybrid Approach Use a backward search with an approximation technique (BDD or whatever). Use the forward exact search and pruning.

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