<p>In recent years, there has been much advancement in the area of verification of infinite-state systems. A system can have an infinite state-space due to unbounded data structures such as counters, clocks, stacks, queues, etc. It may also be infinite-state due to parameterization, i.e., the possibility of having an arbitrary number of components in the system. For parameterized systems, we are interested in checking correctness of all the instances in one verification step. </p><p>In this thesis, we consider systems which contain both sources of infiniteness, namely: (a) real-valued clocks and (b) parameterization. More precisely, we consider two models: (a) the timed Petri net (TPN) model, which is an extension of the classical Petri net model; and (b) the timed network (TN) model in which an arbitrary number of timed automata run in parallel. </p><p>We consider verification of safety properties for timed Petri nets using forward analysis. Since forward analysis is necessarily incomplete, we provide a semi-algorithm augmented with an acceleration technique in order to make it terminate more often on practical examples. Then we consider a number of problems which are generalisations of the corresponding ones for timed automata and Petri nets. For instance, we consider zenoness where we check the existence of an infinite computation with a finite duration. We also consider two variants of boundedness problem: syntactic boundedness in which both live and dead tokens are considered and semantic boundedness where only live tokens are considered. We show that the former problem is decidable while the latter is not. Finally, we show undecidability of LTL model checking both for dense and discrete timed Petri nets. </p><p>Next we consider timed networks. We show undecidability of safety properties in case each component is equipped with two or more clocks. This result contrasts previous decidability result for the case where each component has a single clock. Also ,we show that the problem is decidable when clocks range over the discrete time domain. This decidability result holds when the processes have any finite number of clocks. Furthermore, we outline the border between decidability and undecidability of safety for TNs by considering several syntactic and semantic variants.</p>

In recent years, there has been much advancement in the area of verification of infinite-state systems. A system can have an infinite state-space due to unbounded data structures such as counters, clocks, stacks, queues, etc. It may also be infinite-state due to parameterization, i.e., the possibility of having an arbitrary number of components in the system. For parameterized systems, we are interested in checking correctness of all the instances in one verification step. In this thesis, we consider systems which contain both sources of infiniteness, namely: (a) real-valued clocks and (b) parameterization. More precisely, we consider two models: (a) the timed Petri net (TPN) model, which is an extension of the classical Petri net model; and (b) the timed network (TN) model in which an arbitrary number of timed automata run in parallel. We consider verification of safety properties for timed Petri nets using forward analysis. Since forward analysis is necessarily incomplete, we provide a semi-algorithm augmented with an acceleration technique in order to make it terminate more often on practical examples. Then we consider a number of problems which are generalisations of the corresponding ones for timed automata and Petri nets. For instance, we consider zenoness where we check the existence of an infinite computation with a finite duration. We also consider two variants of boundedness problem: syntactic boundedness in which both live and dead tokens are considered and semantic boundedness where only live tokens are considered. We show that the former problem is decidable while the latter is not. Finally, we show undecidability of LTL model checking both for dense and discrete timed Petri nets. Next we consider timed networks. We show undecidability of safety properties in case each component is equipped with two or more clocks. This result contrasts previous decidability result for the case where each component has a single clock. Also ,we show that the problem is decidable when clocks range over the discrete time domain. This decidability result holds when the processes have any finite number of clocks. Furthermore, we outline the border between decidability and undecidability of safety for TNs by considering several syntactic and semantic variants.