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.

**Read or Download Advances in Verification of Time Petri Nets and Timed Automata: A Temporal Logic Approach PDF**

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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.