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

This monograph provides a complete advent to timed automata (TA) and

time Petri nets (TPNs) which belong to the main established versions of real-time

systems. the various current tools of translating time Petri nets to timed

automata are provided, with a spotlight at the translations that correspond to the

semantics of time Petri nets, associating clocks with quite a few parts 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 in accordance with nation type ways for TPNs

and on partition refinement for TA. additionally, the monograph offers a contemporary growth

in the improvement of 2 version checking equipment, in response to both exploiting

abstract kingdom areas or on program of SAT-based symbolic recommendations.

The booklet addresses study scientists in addition to graduate and PhD scholars

in desktop technological know-how, logics, and engineering of genuine time systems.

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

**Sample text**

8, whereas clock0T (t) = 0 for all t ∈ T . Passing of two time units results in changing the state into σ1T = (m0 , clock1T ), with clock1T (t) = 2 for all t ∈ T . At the state σ1T , ﬁring of both the transitions t1 and t2 is possible. Firing of t1 leads to the state σ2T = (m2 , clock2T ), with m2 (p2 ) = m2 (p3 ) = 1 and m2 (pi ) = 0 for i = 1, 4, 5, 6, 7, 8, and with clock2T (t) = clock1T (t) for all t ∈ T . Firing of t2 at the state σ2T leads to the state σ3T = (m3 , clock3T ), with m3 (p3 ) = m3 (p4 ) = 1 and m3 (pi ) = 0 for i = 1, 2, 5, 6, 7, 8, and with clock3T (t3 ) = 0 and clock3T (t) = clock2T (t) for all t ∈ T \ {t3 }.

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. 2. 2 Networks of Timed Automata In this section we deﬁne timed automata, give their semantics, and show how to deﬁne a product of timed automata.

Such runs are called + (σ) we denote the set of all the progressive strongly strongly monotonic. By fN monotonic σ-runs of N . The set of all the states of N which are reachable on the (progressive12 ) strongly monotonic σ 0 -runs is denoted by Reach+R N , where R ∈ {T, P, N, F } refers to the semantics. A marking m is reachable (on strongly monotonic runs) if there is a state (m, ·) ∈ Reach+R N . The set of all + (again, this set does not the reachable markings of N is denoted by RMN depend on the deﬁnition of the concrete states applied).