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 prevalent types of real-time
systems. many of the latest 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 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 in accordance with nation type ways for TPNs
and on partition refinement for TA. furthermore, the monograph provides a up to date development
in the improvement of 2 version checking equipment, according to both exploiting
abstract kingdom areas or on software of SAT-based symbolic strategies.

The booklet addresses study scientists in addition to graduate and PhD scholars
in laptop technological know-how, logics, and engineering of genuine 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

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 }. Then, passing one unit of time results in the state σ4T = (m3 , clock4T ), with clock4T (t3 ) = 1 and clock4T (t) = 3 for all t ∈ T \ {t3 }. Firing of t3 at σ4T leads to the state σ5T = (m5 , clock5T ), with m5 (p5 ) = m5 (p6 ) = 1 and m5 (pi ) = 0 for i = 1, 2, 3, 4, 7, 8, and with clock5T (t4 ) = clock5T (t5 ) = 0 and clock5T (t) = clock4T (t) for all t ∈ T \ {t4 , t5 }.

A distributed time Petri net with communicating processes (Fischer’s mutual exclusion protocol for n = 2) It is easy to notice that a distributed net is 1-safe. The interpretation of such a net is a collection of sequential, non-deterministic processes with communication capabilities (via joint transitions). , for each Ni and each t ∈ Ti , | • t| = |t • | = 1), which implies that for each i ∈ I there is exactly one p ∈ Pi with m0i (p) > 0 (and, in fact, with m0i (p) = 1), and that in any reachable marking m of N there is exactly one place p of each process with m(p) = 1.

Then, passing one unit of time results in the state σ4T = (m3 , clock4T ), with clock4T (t3 ) = 1 and clock4T (t) = 3 for all t ∈ T \ {t3 }. Firing of t3 at σ4T leads to the state σ5T = (m5 , clock5T ), with m5 (p5 ) = m5 (p6 ) = 1 and m5 (pi ) = 0 for i = 1, 2, 3, 4, 7, 8, and with clock5T (t4 ) = clock5T (t5 ) = 0 and clock5T (t) = clock4T (t) for all t ∈ T \ {t4 , t5 }. Clocks Assigned to the Places Another approach consists in assigning clocks to the places of a net7 . A concrete state σ P of N is then an ordered pair (m, clock P ), where • m is a marking, and • clock P : P −→ IR0+ is a function which for each place p ∈ P gives the time elapsed since p became marked most recently8 .

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