Decision Problems for Petri Nets with Names

We prove several decidability and undecidability results for nu-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of nu-PN strictly surpasses that of P/T nets. We prove that nu-PN are Well Structured Transition Systems. In particular, we obtain decidability of coverability and termination, so that the expressive power of Turing machines is not reached. Moreover, they are strictly Well Structured, so that the boundedness problem is also decidable. We consider two properties, width-boundedness and depth-boundedness, that factorize boundedness. Width-boundedness has already been proven to be decidable. We prove here undecidability of depth-boundedness. Finally, we obtain Ackermann-hardness results for all our decidable decision problems.Comment: 20 pages, 7 figure

Towards Efficient Verification of Elementary Object Systems

Elementary Object Systems (EOS) is a class of Object Petri Nets that follows the “nets-within-nets” paradigm. It combines several practical as well as theoretical properties for the needs of multi-agent-systems. However, it comes with some constraints that limit their expressiveness for automatic verification purposes due to the highly expressive nature of the underlying class of Petri nets. In this paper, we proposed a set of transformation rules from EOS to basic Petri nets nets and show isomorphism of the state spaces in order to make verification feasible

Ordered Navigation on Multi-attributed Data Words

We study temporal logics and automata on multi-attributed data words. Recently, BD-LTL was introduced as a temporal logic on data words extending LTL by navigation along positions of single data values. As allowing for navigation wrt. tuples of data values renders the logic undecidable, we introduce ND-LTL, an extension of BD-LTL by a restricted form of tuple-navigation. While complete ND-LTL is still undecidable, the two natural fragments allowing for either future or past navigation along data values are shown to be Ackermann-hard, yet decidability is obtained by reduction to nested multi-counter systems. To this end, we introduce and study nested variants of data automata as an intermediate model simplifying the constructions. To complement these results we show that imposing the same restrictions on BD-LTL yields two 2ExpSpace-complete fragments while satisfiability for the full logic is known to be as hard as reachability in Petri nets

Towards Efficient Verification of Elementary Object Systems

Elementary Object Systems (EOS) is a class of Object Petri Nets that follows the “nets-within-nets” paradigm. It combines several practical as well as theoretical properties for the needs of multi-agent-systems. However, it comes with some constraints that limit their expressiveness for automatic verification purposes due to the highly expressive nature of the underlying class of Petri nets. In this paper, we proposed a set of transformation rules from EOS to basic Petri nets nets and show isomorphism of the state spaces in order to make veri- fication feasible

Automata Column: The Complexity of Reachability in Vector Addition Systems

International audienceThe program of the 30th Symposium on Logic in Computer Science held in 2015 in Kyoto included two contributions on the computational complexity of the reachability problem for vector addition systems: Blondin, Finkel, Göller, Haase, and McKenzie [2015] attacked the problem by providing the first tight complexity bounds in the case of dimension 2 systems with states, while Leroux and Schmitz [2015] proved the first complexity upper bound in the general case. The purpose of this column is to present the main ideas behind these two results, and more generally survey the current state of affairs

Decidable Models of Recursive Asynchronous Concurrency

Asynchronously communicating pushdown systems (ACPS) that satisfy the empty-stack constraint (a pushdown process may receive only when its stack is empty) are a popular decidable model for recursive programs with asynchronous atomic procedure calls. We study a relaxation of the empty-stack constraint for ACPS that permits concurrency and communication actions at any stack height, called the shaped stack constraint, thus enabling a larger class of concurrent programs to be modelled. We establish a close connection between ACPS with shaped stacks and a novel extension of Petri nets: Nets with Nested Coloured Tokens (NNCTs). Tokens in NNCTs are of two types: simple and complex. Complex tokens carry an arbitrary number of coloured tokens. The rules of NNCT can synchronise complex and simple tokens, inject coloured tokens into a complex token, and eject all tokens of a specified set of colours to predefined places. We show that the coverability problem for NNCTs is Tower-complete. To our knowledge, NNCT is the first extension of Petri nets, in the class of nets with an infinite set of token types, that has primitive recursive coverability. This result implies Tower-completeness of coverability for ACPS with shaped stacks

Data Centric Workflows for Crowdsourcing

International audienc