Computing Optimal Coverability Costs in Priced Timed Petri Nets

We consider timed Petri nets, i.e., unbounded Petri nets where each token carries a real-valued clock. Transition arcs are labeled with time intervals, which specify constraints on the ages of tokens. Our cost model assigns token storage costs per time unit to places, and firing costs to transitions. We study the cost to reach a given control-state. In general, a cost-optimal run may not exist. However, we show that the infimum of the costs is computable.Comment: 26 pages. Contribution to LICS 201

Sampled Semantics of Timed Automata

Sampled semantics of timed automata is a finite approximation of their dense time behavior. While the former is closer to the actual software or hardware systems with a fixed granularity of time, the abstract character of the latter makes it appealing for system modeling and verification. We study one aspect of the relation between these two semantics, namely checking whether the system exhibits some qualitative (untimed) behaviors in the dense time which cannot be reproduced by any implementation with a fixed sampling rate. More formally, the \emph{sampling problem} is to decide whether there is a sampling rate such that all qualitative behaviors (the untimed language) accepted by a given timed automaton in dense time semantics can be also accepted in sampled semantics. We show that this problem is decidable

Adding Time to Pushdown Automata

In this tutorial, we illustrate through examples how we can combine two classical models, namely those of pushdown automata (PDA) and timed automata, in order to obtain timed pushdown automata (TPDA). Furthermore, we describe how the reachability problem for TPDAs can be reduced to the reachability problem for PDAs.Comment: In Proceedings QFM 2012, arXiv:1212.345

Decisive Markov Chains

We consider qualitative and quantitative verification problems for infinite-state Markov chains. We call a Markov chain decisive w.r.t. a given set of target states F if it almost certainly eventually reaches either F or a state from which F can no longer be reached. While all finite Markov chains are trivially decisive (for every set F), this also holds for many classes of infinite Markov chains. Infinite Markov chains which contain a finite attractor are decisive w.r.t. every set F. In particular, this holds for probabilistic lossy channel systems (PLCS). Furthermore, all globally coarse Markov chains are decisive. This class includes probabilistic vector addition systems (PVASS) and probabilistic noisy Turing machines (PNTM). We consider both safety and liveness problems for decisive Markov chains, i.e., the probabilities that a given set of states F is eventually reached or reached infinitely often, respectively. 1. We express the qualitative problems in abstract terms for decisive Markov chains, and show an almost complete picture of its decidability for PLCS, PVASS and PNTM. 2. We also show that the path enumeration algorithm of Iyer and Narasimha terminates for decisive Markov chains and can thus be used to solve the approximate quantitative safety problem. A modified variant of this algorithm solves the approximate quantitative liveness problem. 3. Finally, we show that the exact probability of (repeatedly) reaching F cannot be effectively expressed (in a uniform way) in Tarski-algebra for either PLCS, PVASS or (P)NTM.Comment: 32 pages, 0 figure

Zenoness for Timed Pushdown Automata

Timed pushdown automata are pushdown automata extended with a finite set of real-valued clocks. Additionaly, each symbol in the stack is equipped with a value representing its age. The enabledness of a transition may depend on the values of the clocks and the age of the topmost symbol. Therefore, dense-timed pushdown automata subsume both pushdown automata and timed automata. We have previously shown that the reachability problem for this model is decidable. In this paper, we study the zenoness problem and show that it is EXPTIME-complete.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Petri Nets with Time and Cost

We consider timed Petri nets, i.e., unbounded Petri nets where each token carries a real-valued clock. Transition arcs are labeled with time intervals, which specify constraints on the ages of tokens. Our cost model assigns token storage costs per time unit to places, and firing costs to transitions. We study the cost to reach a given control-state. In general, a cost-optimal run may not exist. However,we show that the infimum of the costs is computable.Comment: In Proceedings Infinity 2012, arXiv:1302.310

Timed Lossy Channel Systems

Lossy channel systems are a classical model with applications ranging from the modeling of communication protocols to programs running on weak memory models. All existing work assume that messages traveling inside the channels are picked from a finite alphabet. In this paper, we extend the model by assuming that each message is equipped with a clock representing the age of the message, thus obtaining the model of Timed Lossy Channel Systems (TLCS). The main contribution of the paper is to show that the control state reachability problem is decidable for TLCS

Data Multi-Pushdown Automata

We extend the classical model of multi-pushdown systems by considering systems that operate on a finite set of variables ranging over natural numbers. The conditions on variables are defined via gap-order constraints that allow to compare variables for equality, or to check that the gap between the values of two variables exceeds a given natural number. Furthermore, each message inside a stack is equipped with a data item representing its value. When a message is pushed to the stack, its value may be defined by a variable. When a message is popped, its value may be copied to a variable. Thus, we obtain a system that is infinite in multiple dimensions, namely we have a number of stacks that may contain an unbounded number of messages each of which is equipped with a natural number. It is well-known that the verification of any non-trivial property of multi-pushdown systems is undecidable, even for two stacks and for a finite data-domain. In this paper, we show the decidability of the reachability problem for the classes of data multi-pushdown system that admit a bounded split-width (or equivalently a bounded tree-width). As an immediate consequence, we obtain decidability for several subclasses of data multi-pushdown systems. These include systems with single stacks, restricted ordering policies on stack operations, bounded scope, bounded phase, and bounded context switches