Formal Modeling and Analysis of Timed Systems: 7th by Nikolaj Bjørner, Leonardo de Moura (auth.), Joël Ouaknine,

By Nikolaj Bjørner, Leonardo de Moura (auth.), Joël Ouaknine, Frits W. Vaandrager (eds.)

This ebook constitutes the refereed court cases of the seventh foreign convention on Formal Modeling and research of Timed platforms, codecs 2009, held in Budapest, Hungary, September 2009.

The 18 revised complete papers offered including four invited talks have been rigorously reviewed and chosen from forty submissions. the purpose of codecs is to advertise the examine of primary and functional points of timed structures, and to assemble researchers from varied disciplines that percentage pursuits within the modelling and research of timed systems.Typical subject matters comprise (but should not restricted to):

– Foundations and Semantics. Theoretical foundations of timed platforms and languages; comparability among diversified versions (timed automata, timed Petri nets, hybrid automata, timed technique algebra, max-plus algebra, probabilistic models).

– tools and instruments. options, algorithms, information constructions, and software program instruments for studying timed platforms and resolving temporal constraints (scheduling, worst-case execution time research, optimization, version checking, trying out, constraint fixing, etc.).

– purposes. variation and specialization of timing know-how in program domain names within which timing performs a huge function (real-time software program, circuits, and difficulties of scheduling in production and telecommunication).

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Extra resources for Formal Modeling and Analysis of Timed Systems: 7th International Conference, FORMATS 2009, Budapest, Hungary, September 14-16, 2009. Proceedings

Example text

C(A) defines “A supervised/restricted by C” and is inductively defined by its set of runs: – (q0 , 0) ∈ Runs(C(A)), e e – if ρ ∈ Runs(C(A)) and ρ −→ s ∈ Runs(A), then ρ −→ s ∈ Runs(C(A)) if one of the following three conditions holds: 1. e ∈ Σu , 2. e ∈ Σc ∩ C(ρ), δ δ 3. t. 0 ≤ δ < e, last(ρ) −→ last(ρ) + δ ∧ λ ∈ C(ρ −→ last(ρ) + δ). C(A) can also be viewed as a TTS where each state is a run of A and the transitions are given by the previous definition. C is a winning controller for (A, Bad) if Reach(C(A)) ∩ Bad = ∅.

6. 7. Transform A into the fleshy region-split form and check that it has 1 12 clock. Write the integral eigenvalue equation (I) with one variable. t. x and get a differential equation (D). Instantiate (I) at 0, and obtain a boundary condition (B). Solve (D) with boundary condition (B). Take ρ = max{λ| a non-0 solution exists}. Return H(L(A)) = log ρ. The detailed algorithm is given in [3], here we only sketch it. Notice first that the set S = {(q, x) | x ∈ rq } is now a disjoint union of unit length intervals and singleton points.

On B. As B is deterministic, D needs only the knowledge of w and we can write D(hw) ignoring the states of A . For B we can even write D(w) instead of D(hw). Define the equivalence relation ≡ on Σ ∗ by: w ≡ w if D(w) = D(w ). Denote the ∗ class of a word w by [w]. Because D is memory bounded, Σ/≡ is of finite index which is exactly the memory needed by D. Thus we can define an automaton D/≡ = q0 (M, m0 , Σ, →) by: M = {[w] | w ∈ Σ ∗ }, • Σl a m0 = [ε], and [w] −−→ [wa] for a ∈ D(hw). h D/≡ is an automaton which accepts L(A) (and it is isomorphic to D(B)) and the size of which is A • the size of D because B has only one state.

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