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

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

This monograph provides a finished advent to timed automata (TA) and
time Petri nets (TPNs) which belong to the main typical versions of real-time
systems. a few of the latest equipment 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 quite a few elements of the
nets. "Advances in Verification of Time Petri Nets and Timed Automata – A Temporal
Logic technique" introduces timed and untimed temporal specification languages
and supplies version abstraction tools according to kingdom category ways for TPNs
and on partition refinement for TA. furthermore, the monograph provides a contemporary development
in the advance of 2 version checking tools, in line with both exploiting
abstract kingdom areas or on program of SAT-based symbolic innovations.

The ebook addresses study scientists in addition to graduate and PhD scholars
in laptop technology, logics, and engineering of actual time systems.

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

Example text

One of them are timed coloured Petri nets [92], in which the time concept is based on introducing a global clock used to represent the model time. Tokens are equipped with time stamps, which describe the earliest model times at which they can be used to fire a transition. Stamps are modified according to expressions associated either with transitions, or with their output arcs. Timing intervals can be interpreted as periods of non-activity of tokens, and the transitions are fired according to the strong earliest firing rule.

Let I = {i1 , . . , inI } be the set indexing the processes of N . A concrete state σ N of N is defined as an ordered pair (m, clock N ), where • m is a marking, and • clock N : I −→ IR0+ is a function which for each index i ∈ I gives the time elapsed since the marked place p ∈ Pi of the process Ni of N became marked most recently. 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).

9. Again, consider the (distributed) net shown in Fig. 3, whose processes are indexed by the set I = {1, 2}, and the sets of places of these processes are P1 = {p1 , p3 , p5 , p7 } and P2 = {p2 , p4 , p6 , p8 }. In the initial state (σ N )0 , m0 (p1 ) = m0 (p2 ) = 1 and m0 (pi ) = 0 for i = 3, . . , 8, whereas clock0N (i) = 0 for all i ∈ I. Passing of two time units results in changing the state into σ1N = (m0 , clock1N ), with clock1N (i) = 2 for all i ∈ I. At the state σ1P , firing of both the transitions t1 and t2 is possible.

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