By Etienne Andre, Romain Soulat(auth.)
ISBN-10: 1118569350
ISBN-13: 9781118569351
ISBN-10: 1848214472
ISBN-13: 9781848214477
This booklet introduces state of the art verification innovations for real-time embedded structures, in accordance with the inverse strategy for parametric timed automata. It studies renowned formalisms for the specification and verification of timed concurrent structures and, specifically, timed automata in addition to numerous extensions akin to timed automata outfitted with stopwatches, linear hybrid automata and affine hybrid automata.
The inverse strategy is brought, and its merits for ensuring robustness in real-time structures are proven. Then, it truly is proven how an generation of the inverse strategy can resolve the nice parameters challenge for parametric timed automata by way of computing a behavioral cartography of the approach. diverse extensions are proposed relatively for hybrid platforms and purposes to scheduling difficulties utilizing timed automata with stopwatches. a variety of examples, either from the literature and undefined, illustrate the options through the book.
Various parametric verifications are played, specifically of abstractions of a reminiscence circuit bought by means of the chipset producer ST-Microelectronics, in addition to of the potential flight regulate method of the subsequent iteration of spacecraft designed via ASTRIUM house Transportation.
Contents:
1. Parametric Timed Automata.
2. The Inverse process for Parametric Timed Automata.
3. The Inverse technique in perform: software to Case Studies.
4. Behavioral Cartography of Timed Automata.
5. Parameter Synthesis for Hybrid Automata.
6. software to the Robustness research of Scheduling Problems.
7. end and Perspectives.
Content:
Chapter 1 Parametric Timed Automata (pages 1–22): Etienne Andre and Romain Soulat
Chapter 2 The Inverse process for Parametric Timed Automata (pages 23–54): Etienne Andre and Romain Soulat
Chapter three The Inverse technique in perform: program to Case stories (pages 55–80): Etienne Andre and Romain Soulat
Chapter four Behavioral Cartography of Timed Automata (pages 81–102): Etienne Andre and Romain Soulat
Chapter five Parameter Synthesis for Hybrid Automata (pages 103–120): Etienne Andre and Romain Soulat
Chapter 6 program to the Robustness research of Scheduling difficulties (pages 121–132): Etienne Andre and Romain Soulat
Chapter 7 end and views (pages 133–136): Etienne Andre and Romain Soulat
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Extra resources for The Inverse Method
Sample text
Post ∗A(K) (S) = i≥0 Post iA(K) (S)). In this book, we will be, in particular, interested in computing the set Post ∗A(K) ({s0 }), where s0 is the initial state of A(K). Note that if ∪i j then Post ∗A(K) ({s0 }) = Post i+1 ⊑ j=0 Post A(K) ({s0 })), A(K) ({s0 }) ∪i j j=0 Post A(K) ({s0 }). 2. Traces The notion of trace associated with a concrete run, and the notion of trace set associated with a timed automaton apply in a straightforward manner to parametric timed automata. – Given a parametric timed automaton A and a symbolic run r am−1 a of A of the form (q0 , C0 ) ⇒0 · · · ⇒ (qm , Cm ), the trace associated with r is the am−1 a alternating sequence of locations and actions q0 ⇒0 · · · ⇒ qm .
4. 4, containing two clocks x1 and x2 , two parameters p1 and p2 and a single state q0 with invariant x1 ≤ p1 . Consider the following reference valuation π0 of the parameters: {p1 = 3, p2 = 1}. 5(a), is made up of three self-transitions from q0 . Let us apply the inverse method to A and π0 . Consider for the sake of simplicity that we have initially x1 = x2 = 0. Then, the initial state after time elapsing is (q0 , C0 ), with C0 : x2 = x1 ∧ x1 ≥ 0 ∧ p1 ≥ x1 . After one iteration of IM , the state (q0 , C1 ) is reachable, with C1 : x1 ≥ x2 + p2 ∧ x2 ≥ 0 ∧ x1 ≥ x2 ∧ p1 ≥ x1 .
We will see in Chapter 4 how the inverse method solving this inverse problem can be used to solve the good parameters problem. 2. 1. Principle We introduce in the following the inverse method [AND 09c], which is a solution to the inverse problem stated above. The inverse method consists of generating runs starting from the initial state, and removing states incompatible with the reference values by appropriately refining the current constraint K0 on the parameters. The generation procedure is then restarted until a new incompatible state is produced, and so on, iteratively until no incompatible state is generated.