Numerical grid generation techniques : proceedings of a workshop held at NASA Langley Research Center, Hampton, Virginia, October 6-7, 1980 /

Includes bibliographical references.

Soundness of workflow nets: classification, decidability, and analysis

Workflow nets, a particular class of Petri nets, have become one of the standard ways to model and analyze workflows. Typically, they are used as an abstraction of the workflow that is used to check the so-called soundness property. This property guarantees the absence of livelocks, deadlocks, and other anomalies that can be detected without domain knowledge. Several authors have proposed alternative notions of soundness and have suggested to use more expressive languages, e.g., models with cancellations or priorities. This paper provides an overview of the different notions of soundness and investigates these in the presence of different extensions of workflow nets.We will show that the eight soundness notions described in the literature are decidable for workflow nets. However, most extensions will make all of these notions undecidable. These new results show the theoretical limits of workflow verification. Moreover, we discuss some of the analysis approaches described in the literature.

Reduction rules for reset/inhibitor nets

Reset/inhibitor nets are Petri nets extended with reset arcs and inhibitor arcs. These extensions can be used to model cancellation and blocking. A reset arc allows a transition to remove all tokens from a certain place when the transition fires. An inhibitor arc can stop a transition from being enabled if the place contains one or more tokens. While reset/inhibitor nets increase the expressive power of Petri nets, they also result in increased complexity of analysis techniques. One way of speeding up Petri net analysis is to apply reduction rules. Unfortunately, many of the rules defined for classical Petri nets do not hold in the presence of reset and/or inhibitor arcs. Moreover, new rules can be added. This is the first paper systematically presenting a comprehensive set of reduction rules for reset/inhibitor nets. These rules are liveness and boundedness preserving and are able to dramatically reduce models and their state spaces. It can be observed that most of the modeling languages used in practice have features related to cancellation and blocking. Therefore, this work is highly relevant for all kinds of application areas where analysis is currently intractable.

A new methodology for analyzing distributed systems modeled by petri nets

Distributed computing systems can be modeled adequately by Petri nets. The computation of invariants of Petri nets becomes necessary for proving the properties of modeled systems. This paper presents a two-phase, bottom-up approach for invariant computation and analysis of Petri nets. In the first phase, a newly defined subnet, called the RP-subnet, with an invariant is chosen. In the second phase, the selected RP-subnet is analyzed. Our methodology is illustrated with two examples viz., the dining philosophers' problem and the connection-disconnection phase of a transport protocol. We believe that this new method, which is computationally no worse than the existing techniques, would simplify the analysis of many practical distributed systems.

Non-tactical symmetric nets

Mavron, Vassili; Al-Kenani, A.N., (2003) 'Non-tactical symmetric nets', Journal of the London Mathematical Society 67(2) pp.273-288 RAE2008

Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

Differential Priors for Elastic Nets

The elastic net and related algorithms, such as generative topographic mapping, are key methods for discretized dimension-reduction problems. At their heart are priors that specify the expected topological and geometric properties of the maps. However, up to now, only a very small subset of possible priors has been considered. Here we study a much more general family originating from discrete, high-order derivative operators. We show theoretically that the form of the discrete approximation to the derivative used has a crucial influence on the resulting map. Using a new and more powerful iterative elastic net algorithm, we confirm these results empirically, and illustrate how different priors affect the form of simulated ocular dominance columns.

Generalized Nets Model of an E-Learning System Software Architecture

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshko ff and Lubomir Tschakaloff , Sofi a, July, 2006.

Compositions, Generated by Special Nets in Affinely Connected Spaces

Special nets which characterize Cartesian, geodesic, Chebyshevian, geodesic- Chebyshevian and Chebyshevian-geodesic compositions are introduced. Con- ditions for the coefficients of the connectedness in the parameters of these special nets are found.

Using coloured petri nets to simulate DoS-resistant protocols

In this work, we examine unbalanced computation between an initiator and a responder that leads to resource exhaustion attacks in key exchange protocols. We construct models for two cryp-tographic protocols; one is the well-known Internet protocol named Secure Socket Layer (SSL) protocol, and the other one is the Host Identity Protocol (HIP) which has built-in DoS-resistant mechanisms. To examine such protocols, we develop a formal framework based on Timed Coloured Petri Nets (Timed CPNs) and use a simulation approach provided in CPN Tools to achieve a formal analysis. By adopting the key idea of Meadows' cost-based framework and re¯ning the de¯nition of operational costs during the protocol execution, our simulation provides an accurate cost estimate of protocol execution compar- ing among principals, as well as the percentage of successful connections from legitimate users, under four di®erent strategies of DoS attack.