**4.1 Declaration**

The operation of the colored Petri net shown in **Figure 7** is described in more

*Interrelation of colored petri nets and traditional languages. (CPNL, language of colored petri net).*

<sup>Т</sup>he colored Petri net (**Figure 7**), which is built for *<sup>L</sup>*<sup>∗</sup> <sup>¼</sup> *<sup>L</sup>* <sup>∪</sup> *LL* <sup>∪</sup> *LLL* … language, suggests the following relationship between the languages of the colored Petri nets with some classes of traditional languages (see **Figure 8**) [10].

The Venn diagram, modified by the author (**Figure 8**), shows the relationship between the languages of the colored Petri nets and some traditional languages. This fact illustrates that the language class of colored Petri nets includes an entire class of

In 1971 Patil proved that P and V actions have insufficient capacity for resolving synchronization issues. His proposed solution to model problem is called smoking

Let X be the smoker with tobacco, Y the smoker with paper, Z the smoker with

It is proven that the problem of smokers has no solution using semaphores [9]. Patil showed that there is no sequence of P and V actions to correctly solve the

The author simulated a problem with the colored Petri net (see**Figure 9**) [3–6, 9, 18, 19]. The operation of the colored Petri net shown in **Figure 9** is described in more

If we were to represent this problem using the classical Petri net, then we need to use three transitions instead of one **T** transition. It also means that minimization of the network is ensured, which implies a reduction in costs due to the reduction of

**Processes AX Processes AY Processes AZ**

Pick up the tobacco Pick up the match Roll the cigarette Light the cigarette Smoke the cigarette Return to AY

Pick up the tobacco Pick up the paper Roll the cigarette Light the cigarette Smoke the cigarette Return to AZ

**4. On a solution to the cigarette smoker's problem with colored**

The actions of the smokers without the coordination are as follows.

problem [1, 2]. Modeling the problem using the classical Petri net, we get an inactive network. Since all tokens in classical Petri nets are of the same type, the

detail in the literature [3, 10].

*Numerical Modeling and Computer Simulation*

languages without context.

matches, and A the agent (see **Table 1**).

ingredients will not differ from each other.

detail in the literature [9].

Pick up the paper Pick up the match Roll the cigarette Light the cigarette Smoke the cigarette Return to AX

*The actions of the smokers.*

**Table 1.**

**126**

arches in positions and transitions.

**Petri nets**

**Figure 8.**

a cigarette [9].

Color INT ¼ integer; Color U ¼ t; Color N ¼ P; Color Q ¼ m; Color E <sup>¼</sup> Product N<sup>∗</sup> Q OR Product U<sup>∗</sup> Q OR Product N<sup>∗</sup> f g <sup>U</sup> ; Var K, l ð Þ : E; n : INT;

### **4.2 Conclusion**

In the problem, we identify certain advantages of colored Petri net to P and V operations and classical Petri net with the synchronization problem. The mentioned studies allow identification of synchronization modeling opportunities with the help of colored Petri net.
