 Zdaj imam tudi izgleda, tudi izgleda z Angelo Montanari in Laura Bozzelli, z Universtvim Vudine in z Universtvim Naplesem. Fokus v pippa je na temporalne planiče, ali vzgleda, da ne izgleda vzgleda vzgleda, če je vzgleda na akciju, če je vzgleda na timeline. zelo zelo vzoutenite vzoutenite vzouti, vzoutenite vzouti, in zelo vzoutenite, in zelo vzouti. Tudi da res nekako še krativno je proč, da poživimo začniti. Tudi je to početnit, da je zelo cestil od presnega začniti, in zelo zelo zelo, da je zelo vzouto na vzouti, na zelo vzouti na zelo vzouti, The temporal domain setting. In the discrete temporal domain setting, we have the problem, the decision problem. If there is a set of a timeline which satisfies all the constraints given in the specification, it is in X-piece phase. It can be solved in X-piece phase. In the case of a dense temporal domain, which is the domain where we are focusing, Sveč je vzgleda, da je izgleda nekaj problem. Zato nekaj, da je izgleda z다는i, semantik, semantik, semantik začel. Vzgledaj smo, da je pravno postavljen, semantik začel, začel, v početku o početku, vzitec, tudi je bilo, kako je kaj je pri vsebih, v tega priča, načinno sega vseba je, da je tudi, nekaj je vseba, načinno sega, naj auto početka, od vseba, ko je, da je, da je, da je, da je, da je, da je. Jed Perhaps it proved it is reasonable from computational point of view since it is, we have proved it a problem is in p-space. Essentially by reduction to time of the automata so complexity is the same as reference for formalism for dense time domains. And we believe it is expressive for practical point of view. In druga kontribušnja je izgleda in izgleda in izgleda, kaj smo vzalivali, da vzalivamo konverso, da vzalivamo konverso z definiciju, za predstavljenju, za vzalivanje za vzalivanje vzalivanje vzalivanje vzalivanje vzalivanje vzalivanje vzalivanje vzalivanje vzalivanje. Vzalivamo konverso z vzalivanjem, da vzalivamo konverso vzalivanje. V tako počusti bomo zelo na prejmojnjo vsega, nekaj, da se priče vsega vržitega. In bomo počusti nekaj vsega, najbolj vsega, ki je vsega zelo, nekaj se vsega, nekaj se priče, nekaj se priče, nekaj se priče, nekaj se priče. In druga segnonizacija je, da when the processor tries to read the first value, it is reading, then this trial has two possible effects. The reading can be unsuccessful, so we have the first disjunct, and then the state remains unchanged, read zero, or the reading attempt is successful, and then the next state is really one, but the condition for a successful read is that the reading token covers a ready state for the sensor. The same, we have a goal, which requires that finally we have two reads and a successful transmission. So we can have the formal definition of the problem. TP domain is a pair where we have a set of variables, a set of rules, and the problem is to answer the question whether there is a multi-time line satisfying all the required constraint or the rule, trigger and trigger as a rule. Unfortunately, the problem in the general setting of this domain is that it has been proved to be undecidable, so we have to consider restriction to gain the desedability of the problem. Here we can have a picture of the result for the problem, for the restriction of the problem. We can find in the, which are of previous results, the starting results for the work I am presenting. The restriction, which have been considered, are the following. First of all, we have considered a semantic restriction, namely called future semantics. In the future semantics, when having fixed a trigger, an atom for trigger, one can choose for the existential part a token in the future, cannot choose a token in the past. Then we have a syntactic restriction, which is called simple rules. It means that the same existential token cannot occur more than once in an existential statement. Then we have a restriction, we have considered a restriction on intervals. Singular intervals are intervals, which are points, essentially, and then points are avoided in the expression of rules. And then we have another restriction on intervals. In this class of intervals, we have intervals, which are either unbounded, or if they are bounded, they start from the initial point, they start from zero. This is the picture in the case of unrestricted semantics. We know that the problem is indecidable. It is indecidable also in the future semantic. So we have to add a restriction on rules. And in the case of future semantic and simple trigger rules, we have a decidable problem, but the complexity is very high, since it is non-primitive and recursive. But if you consider simple trigger rules and don't singular intervals, the problem is easier. The complexity is proven to be X-space and X-space complete. And in the case of the more restricted set of intervals, the problem is in P-spains. There is also another interesting result. If you consider only trigger-less rules, the problem is NP-complete. But of course trigger rules are not enough to express meaningful specifications. So one cannot consider this formula with this very strong restriction. Now we have considered another alternative semantic, which do not require any syntactic restriction on the rule format. And the semantics is based on this idea. That when one issue a trigger, each trigger requires something which requires a response in a science from another token. And the response has to happen as soon as possible. It has been a prompt response. So in this case, when we ask, we fix this trigger, this trigger for this token, we can satisfy the requirement both choosing for B and C, both choosing this occurrence or this occurrence of the token. In the prompt semantics in a sense, we cannot choose the second instance, but we have to choose the first one. We are obliged to choose the first one. We have the idea that in the existential part the chosen token must be as much as the closest token. But what does it mean closest? We have to fix precisely the idea of closest token and fix the definition of closest token. We have two alternatives. We have investigated two alternatives. The first one is the strong minimal semantics. It leads to the strong minimal semantics. The idea is that when we have to choose a token, we have to choose the token which minimizes the distance, whose starting point minimizes the distance from the starting point of the trigger. This simple definition leads to a very powerful setting. This is shown in this example. If we have a simple timeline with only one value for the state, C, and then we have a swap for A and B in the previous timeline, what it is required, it is very simple, that for each occurrence of A of B, there must be both a C preceding B and another C following B. But this is possible only if the distance in between the starting point of the first occurrence from the token and the distance from the following token from the beginning is the same. Only in this case we can satisfy this constraint. This means that the only solution for this specification is this solution where A and B have the same duration, are constrained to have the same duration, and C is the sum of the duration of A of B. Namely, it is a duration which is two times the duration of B. This simple trick allows to encode counters and to prove that there is a reduction of the halting problem of Minsky to counters machine to the problem, to the tp problem with the strong minimal semantics. This is not a good solution for what we are asking for. We have considered another variant called minimal weak semantics, where we have distinguished the future and the past, requiring that simply when you want to choose a token in the future, one has to choose a token in such a way that there is no token of the same value in between the trigger and the chosen token. In this case we have to choose that if this one is the token and we have a wandering for B, we cannot choose this instance of B. We have to choose this one and the same for C. In this case a similar rule for the past. We have a similar constraint for the past. In this case we have the good news since the problem with this kind of semantics can be shown to be decidable and in particular the problem is it has been proved to be p-space complete. The complete p-space, the upper bound of the problem has been proved from a reduction from the tp problem to time at automata, which exploit a variant of extended evident clock automata, which has been providing this work. Instead the lower bound it has been proved by a technical machinery, which exploit, namely a reduction from a domino tiling problem with linear length of roads into our problem. What is interesting probably is having an idea of the extension of evident clock automata, evident clock automata are a robust fragment of a time automata, which is well known. Robustness depends even on the fact that the values of clocks are fixed by the input and not by the behavior of the automaton. In particular for each symbol of the alphabet we have a past clock and a predicting clock. We have reached this event clock with diagonal constraints. Diagonal constraints are of this form. We have an essential difference of clocks of the same polarity, namely either they are predicting or they are past, not mixed combinations and sums of constraints for tokens of the same, of different polarity. If we remove this constraint on polarity we have another extension which is called ekI++. The properties are that the extension is proper since there is an example of an automaton of a language which cannot be recognized by an event clock automata. And they have the same closure properties. And there is, of course, which is the basic machinery to prove the result. One can take an extended event clock automaton and translate it to a time automaton in exponential time. This automaton has a linear number of clocks and an exponential number of states as it happens for the standard ek. And the nice result is also the curiosity result is also that in the case of ekI++ this conversion cannot be done since the emptiness problem for this class of automata is undecidable. So, we have followed, to prove the main result we have followed these steps. We have encoded, of course, multi-time lines into time awards. We have encoded trigger rules by ekI++. We have encoded trigger rules by standard time automaton and then we have solved the problem in a standard way using the standard machinery for time automaton. And this is the formulation of the main theorem with precise complexity of the states and the clocks. So, in this work we have proposed an alternative semantics for time line, which does not use a restriction of, syntactical restriction of rules and which is meaningful from the possibility of having the specification, of reasonable specification. We have provided an extension of even the clock automaton to extension, one is interesting, the other is indecidable. And as a future work you want to face the problem of model checking using timelines as a basic way to specify systems so we have to have an alternative to point-based definition by means of LTS by label transition system and instead of having timelines as the semantics to be checked. And using an interval model logic like, for instance, Alper and Schoen logic we have investigated in other context which performing a meaningful use of an interval point logic instead of a point-based model logic like LTIL or LCTL and so on. So, that's all. And as you have extended this even clock automaton in CA plus, in CA plus plus, right? Yeah. Now, even clock automaton had nice properties, you know, they were determinizable, closed under compliments. Yes, it is true, I have no detail, but it is true. But it is true both for both the extensions, for both the extensions. But what is not true for the most powerful extension is the conversion to time of automaton and they are, in general, the emptiness problem isn't decidable. Secondly, yeah, I... Considering your logic, you know, with width constraints, you know, translating something to something like MIT, would be... Expressively, is there any relationship? We have... We have a user... It is not... We have extended even the clock automaton since the update of clocks is very, very similar to the idea of promptness, of promptness of the semantic. So it was a natural formalism to have a translation from the setting towards time of automaton. We have... Probably we have investigated model... We have used... We have tried a model checking approach, which uses the metric interval temporal logic to express properties of timelines, using this fragment. And they exploit the same good property that the meter can be encoded by time of automaton. So you can have the solution of model problems, of model checking problem using intersection of time of automaton. So it is the natural logic to speak about this kind of... I do not know if we can do the same with the new semantics. Since we have this minimality constraint, we have to, in a sense, to take care of. Okay? Yeah. What are the parameters synthesis? In some sense? Rules can have parameters. And are there... No, there are no parameters. There is an extendable code. If you want to make me better, I will send you to investigate.