Download Advances in Verification of Time Petri Nets and Timed by Doc.dr.hab. Wojciech Penczek, Dr. Agata Pólrola (auth.) PDF

By Doc.dr.hab. Wojciech Penczek, Dr. Agata Pólrola (auth.)

This monograph offers a entire advent to timed automata (TA) and
time Petri nets (TPNs) which belong to the main favourite types of real-time
systems. many of the current tools of translating time Petri nets to timed
automata are awarded, with a spotlight at the translations that correspond to the
semantics of time Petri nets, associating clocks with a number of elements of the
nets. "Advances in Verification of Time Petri Nets and Timed Automata – A Temporal
Logic method" introduces timed and untimed temporal specification languages
and supplies version abstraction equipment according to kingdom type ways for TPNs
and on partition refinement for TA. furthermore, the monograph provides a up to date growth
in the improvement of 2 version checking tools, in keeping with both exploiting
abstract kingdom areas or on software of SAT-based symbolic thoughts.

The publication addresses learn scientists in addition to graduate and PhD scholars
in desktop technological know-how, logics, and engineering of actual time systems.

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Additional info for Advances in Verification of Time Petri Nets and Timed Automata: A Temporal Logic Approach

Example text

For δ ∈ IR0+ , by clock N + δ we denote the function given by (clock N + δ)(i) = clock N (i)+δ for all i ∈ I. Moreover, let (m, clock N )+δ denote (m, clock N +δ). The (dense) concrete state space of N is now a transition system CcN (N ) = (Σ N , (σ N )0 , →N c ), where • Σ N is the set of all the concrete states of N , • (σ N )0 = (m0 , clock0N ) with clock0N (i) = 0 for each i ∈ I is the initial state, and • a timed consecution relation →N c ⊆ Σ N × (T ∪ IR0+ ) × Σ N is defined by action- and time successors as follows: δ – for δ ∈ IR0+ , (m, clock N ) →N c (m, clock N + δ) iff · for each t ∈ en(m) there exists i ∈ I with •t ∩ Pi = ∅ such that (clock N + δ)(i) ≤ Lf t(t) (time successor), t – for t ∈ T , (m, clock N ) →N c (m1 , clock1N ) iff · t ∈ en(m), · for each i ∈ I with •t ∩ Pi = ∅ we have clock N (i) ≥ Ef t(t), · there is i ∈ I with •t ∩ Pi = ∅ such that clock N (i) ≤ Lf t(t), · m1 = m[t , and · for all i ∈ I we have clock1N (i) = 0 if •t ∩ Pi = ∅ and clock1N (i) = clock N (i) otherwise (action successor).

By a partition of a set B we mean a family of its disjoint subsets B such that B = B. B ∈B 32 • • • • 2 Timed Automata X Z := {v ∈ IRn0+ | (∃v ∈ Z) v ≤ v}, Z ⇑ Z = {v ∈ Z | (∃v ∈ Z ) v ≤ v ∧ (∀v ≤ v ≤ v ) v ∈ Z ∪ Z }, Z[X := 0] = {v[X := 0] | v ∈ Z}, X | v[X := 0] ∈ Z}. , Z[X := 0] and [X := 0]Z) and the standard intersection preserve zones [8, 159]. A description of the implementation of Z\Z , following [8], is given also in Sect. 3. Some examples of the operations are presented in Fig. 2. x2 x2 5 x2 Z \ Z = {Z1 , Z2 } 7 6 Z \ Z = {Z1 , Z2 , Z3 } 6 6 Z3 Z Z Z1 3 3 1 1 3 4 6 x1 x2 Z1 3 Z2 1 3 4 5 6 x1 x2 6 Z2 3 4 5 6 x1 6 x1 x2 6 6 Z Z ∩Z 3 Z 3 1 x1 3 4 x1 3 2 x2 x2 x2 6 6 6 Z⇑Z 3 3 Z ⇑Z Z[x1 := 0] 1 3 4 x1 x2 4 x1 x1 x2 x2 7 Z [x1 := 0] 5 [x1 := 0]Z = ∅ [x1 := 0]Z 3 3 x1 x1 Fig.

The bounds of the firing interval for a transition t ∈ en(m) are, respectively, the minimal and maximal time remaining before firing this transition. Notice, however, that this is not necessarily the one-to-one correspondence. On the one hand, the states (m, clockT ), (m, clock1T ) ∈ Σ T satisfying (∀t ∈ en(m)) clock T (t) = clock1T (t) correspond to the same state σ F ∈ Σ F . On the other hand, in the case when t ∈ en(m) and Lf t(t) = ∞, for all the states with clock T (t) ≥ Ef t(t) the corresponding firing interval is given by f i(t) = [0, ∞).

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