... domain for static analysis by abstract interpretation. It extends a former numerical abstract domain based on Difference-Bound Matrices and allows us to represent invariants of the form (±x ± y ≤ c), where x and y are program variables and c is a real constant. We focus on giving an efficient representation based on Difference-Bound Matrices—O(n²) memory cost, where n is the number of variables—and graph-based algorithms for all common abstract operators—O(n³) time cost. This includes a normal form algorithm to test equivalence of representation and a widening operator to compute least fixpoint approximations.

This paper is concerned with specifying and proving correct systems in which time appears as a parameter. We model such systems via Merlin's Time Petri Nets. An enumerative analysis technique is introduced for these nets based on the computation of a set of state classes and a reachability relation on the set. State classes are de ned in the text and an algorithm is provided for their enumeration. This enumerative approach allows us to derive a nite representation of their behavior for a large family of Time Petri Nets. The analysis method is illustrated by the analysis of a communication protocol

Abstract. Time Petri Nets (TPN) and Timed Automata (TA) are widely-used formalisms for the modeling and analysis of timed systems. A recently-developed approach for the analysis of TPNs concerns their translation to TAs, at which point efficient analysis tools for TAs can then be applied. One feature of much of this previous work has been the use of timed reachability analysis on the TPN in order to construct the TA. In this paper we present a method for the translation from TPNs to TAs which bypasses the timed reachability analysis step. Instead, our method relies on the reachability graph of the underlying untimed Petri net. We show that our approach is competitive for the translation of a wide class of TPNs to TAs in comparison with previous approaches, both with regard to the time required to perform the translation, and with regard to the number of locations and clocks of the produced TA. 1

Timed (or Stochastic) Data Flow Diagrams (TDFD's or SDFD's) introduced in [SB96b] are an extension of the Formalized Data Flow Diagrams, defined in [LWBL96]. This extension allows us to assess the quantitative behavior (e. g., performance, throughput, average load of a bubble, etc.) as well as the qualitative behavior (e. g., deadlock, reachability, termination, finiteness, liveness, etc.), eventually depending on different types of transition times, for the system modeled through the TDFD. In this paper, we consider Markovian transition times for the consumption of in--flow items and for the production of items on the out--flow. Moreover, we require the TDFD to be periodic and irreducible and it must have a finite reachability set. For these models, we have been able to apply an aggregation principle of [Sch84], extended for periodic Markov chains by [Woo93], to efficiently determine stationary probabilities, expected waiting times, and limiting process probabilities. 2 1.1 Introduc...

This article gives an introduction to time extensions of Petri nets. Two popular methods for adding time to Petri nets are presented, and are shown to be equivalent for most cases. The problem of bounding the execution time for these extensions is discussed. Numerous references are given to further reading in each area covered.

Time Petri Nets (TPN) and Timed Automata (TA) are widely-used formalisms for the modeling and analysis of timed systems. A recently-developed approach for the analysis of TPNs concerns their translation to TAs, at which point efficient analysis tools for TAs can then be applied. One feature of much of this previous work has been the use of timed reachability analysis on the TPN in order to construct the TA. In this paper we present a method for the translation from TPNs to TAs which bypasses the timed reachability analysis step. Instead, our method relies on the reachability graph of the underlying untimed Petri net. We show that our approach is competitive for the translation of a wide class of TPNs to TAs in comparison with previous approaches, both with regard to the time required to perform the translation, and with regard to the number of locations and clocks of the produced TA.