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1
Content available remote Petri Net Controlled Finite Automata
Farwer B., Jantzen M., Kudlek M., Rölke H., Zetzsche G.
Fundamenta Informaticae
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2008
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Vol. 85, nr 1-4
111-121
EN
We present a generalization of finite automata using Petri nets as control, called Concurrent Finite Automata for short. Several modes of acceptance, defined by final markings of the Petri net, are introduced, and their equivalence is shown. The class of languages obtained by l-free concurrent finite automata contains both the class of regular sets and the class of Petri net languages defined by final marking, and is contained in the class of context-sensitive languages.
2
Content available remote Concurrent Turing Machines
Farwer B., Kudlek M., Rölke H.
Fundamenta Informaticae
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2007
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Vol. 79, nr 3-4
303-317
EN
We define Concurrent Turing Machines (CTMs) as Turing machines with Petri nets as finite control. This leads to machines with arbitrary many tape heads, thus subsuming any class of (constant) k-head Turing machines. Space, time, and head complexity classes are introduced and discussed showing the difference of various acceptance conditions that are defined for CTMs. Nevertheless, we show that CTMs can be simulated by TMs. Concurrent Turing machines correspond to a class of multiset rewriting systems. The definition of a CTMs as a rewrite theory avoids the need for encoding multisets as words and using an equivalence relation on configurations. Multiset rewriting lends itself to be used in rewriting systems and tools like the rewriting engine Maude. For the rewriting system, a configuration is given by a varying sequence of strings and multisets.
3
Content available remote Separation of Control and Data Flow in High-Level Petri Nets: Transforming Dual Flow Nets into Object Petri Nets
Farwer B., Varea M.
Fundamenta Informaticae
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2006
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Vol. 72, nr 1-3
123-137
EN
This paper summarises two approaches, Dual Flow Nets (DFN) and Object Petri Nets (OPN), and offers a translation mechanism between them. While the DFN model tackles the separation of control and data flow computing aspects, the OPN model has a more generalised structure. The separation between control and data flow can enhance the readability of models, and allows different tools to operate on distinct parts of the model. The aim of this paper is to show how the modelling based on control/data-flow analysis can benefit from an object-based Petri net approach. Tool support and a translation mechanism that is faithful are presented, giving an extra dimension (hierarchy) to the existing paradigm of control and data flow interacting in a model. Our methodology provides a comprehensive separation of these two parts, which can be used to feed analysis or synthesis tools, while still being able to reason about both parts through formal methods of verification.
4
Content available remote Modelling Global and Local Name Spaces for Mobile Agents Using Object Nets
Farwer B., Köhler M.
Fundamenta Informaticae
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2006
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Vol. 72, nr 1-3
109-122
EN
While it often makes sense to use pointer-based semantics (sometimes called reference semantics) to model components of a system that are in close proximity, this kind of modelling becomes increasingly infeasible for distant components. The notion of distance here is to be seen relative with respect to the system being modelled. We use local and global name spaces to model the necessary paradigm shift for systems of communicating mobile agents. As a concrete example of modelling that requires discrimination of notions of proximity or distance, we study a scenario of mobile devices with wireless communications capabilities. The communication can be done directly between two agents or via a system of wireless network routers. To model such a system, we introduce object Petri nets that integrate both semantic paradigms found in the literature, i.e. reference semantics and value semantics. Formal definitions are given and some basic properties are proved.
5
Content available remote Petri Net Processes for Zero-Safe Nets
Farwer B., Köhler M.
Fundamenta Informaticae
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2005
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Vol. 67, nr 1-3
65--75
EN
Composition of modules to larger units is a technique frequently used during the software development life cycle. It is mostly used in a "bottom up" fashion, suggested by the principles of object orientation, where the composition of simple objects to a complex one plays a central role. Composition in Petri nets has been studied in the form of place and transition fusion. Zero-Safe Nets represent a special approach, which allows the use of more complex synchronisation structures, so-called transactions. The definition of transactions is based on interleaving semantics, i.e. on firing-sequences. Problems arise, since the definition is not closed with respect to the permutation of actions. This paper presents a partial order concurrency semantics for zero-safe nets based on Petri net processes. Using these semantics, a characterisation of such transactions closed with respect to permutation of concurrent actions becomes possible.
6
Content available remote Mobile Object-Net Systems and their Processes
Farwer B., Köhler M.
Fundamenta Informaticae
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2004
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Vol. 60, nr 1-4
113--129
EN
The Petri-net-based formalism of mobile object-net systems ( MONS) is used to model concurrent systems with dynamically changing environments, such as mobile objects. The tokens in MONS are themselves Petri nets, which gives the formalism an additional (vertical) dimension of nesting. Traditional Petri nets have essentially a horizontal structure, given by the fact that markings are multisets. The question arises, whether MONS can be regarded as a canonical extension of such Petri nets. Due to the nested nature of MONS, the answer is not obvious. We first give the formal definition of MONS and then prove some properties of the formalism, showing that, with respect to interleaving semantics (i.e. firing sequences), MONS can indeed be viewed as a canonical extension of traditional Petri nets. We then define MONS processes, also as a canonical extension of standard Petri net processes.
7
Content available remote A New Synchronisation Model for Multi-Level Object Petri Nets
Farwer B., Kudlek M.
Fundamenta Informaticae
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2004
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Vol. 60, nr 1-4
131--142
EN
The present paper continues work from [7]. One goal of this work is to find a class of (object) Petri nets of lesser power than Turing machines, such that there exists a universal Petri net within that class. Another goal is to surpass the restricted synchronisation of transitions in object and system nets in the case of value semantics. Finally, an encoding of the proposed class of object Petri nets into linear logic Petri nets (LLPNs) is given, which directly leads to a specification that can be model-checked by existing tools.
8
Content available remote Some Considerations on Higher-Order Petri Nets
Farwer B., Kudlek M., Misra K.
Fundamenta Informaticae
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2003
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Vol. 54, nr 2,3
185-193
EN
This paper introduces higher-order Petri nets based on multiset rewriting. Some variations of the firing rule for high-level Petri nets following the nets-within-nets paradigm, i.e. allowing Petri nets as tokens, are discussed. All considerations keep in mind the possibile existence of a universal higher-order Petri net.
9
Content available remote Modelling with Hierarchical Object Petri Nets
Farwer B., Misra K.
Fundamenta Informaticae
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2003
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Vol. 55, nr 2
129-147
EN
Fehling's hierarchical Petri nets are a net modelling framework based on refinement and abstraction of nets. Object Petri nets are a Petri net-based method of encapsulation. We bring these two domains together in the new concept of hierarchical object Petri nets. Defining hierarchical object Petri nets forces us to consider what it means to preserve synchronisation when abstracting or refining an object Petri net. The goal is to provide a sound theoretical basis for building computer tools to develop high-level Petri net models following the nets-within-nets paradigm.
10
Content available remote Dynamic Modification of Object Petri Nets. An Application to Modelling Protocols with Fork-Join Structures
Farwer B.
Fundamenta Informaticae
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2002
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Vol. 51, nr 1,2
91-101
EN
In this paper we discuss possibilities of modelling protocols by objects in object-based high-level Petri nets. Some advantages of dynamically modifying the structure of token objects are discussed and the need for further investigations into mathematically rigorous foundations of object net formalisms incorporating facilities for such operations on its token nets is emphasised.
11
Content available remote Comparing Concepts of Object Petri Net Formalisms
Farwer B.
Fundamenta Informaticae
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2001
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Vol. 47, nr 3,4
247-258
EN
In recent years many authors have come up with definitions of object Petri nets. They can be divided into two main classes: those that try to model object-orientation within a framework of Petri nets, and those modelling the token objects of an environment net by Petri nets but do not follow the paradigm of object-orientation. We compare some aspects of the latter kind with the foundations of Linear Logic and Linear Logic Petri nets, establishing some simulations between the formalisms
12
Content available remote A Multi-region Linear Logic based calculus for dynamic Petri net structures
Farwer B.
Fundamenta Informaticae
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2000
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Vol. 43, Nr 1-4
61-79
EN
Object based Petri nets are becoming increasingly popular in many fields of computer science. The possibility to model real-world objects as separate Petri nets supports the need for modular design of complex systems. So far object net approaches have been based on the presumption that the object nets' structure remains unchanged in all processes. This paper sheds some light on possible extensions of high-level Petri nets to incorpo-rate the dynamical evolution of Petri net structures. The exposition is based on the Linear Logic encoding of Petri nets, and coloured Petri nets. It provides a basic se-mantics for modifying net structures which can be employed in a framework of nets within nets, i.e. situations where Petri nets (so-called token nets) themselves are used as tokens in an underlying environment net.
13
Content available remote A Linear Logic view of object Petri Nets
Farwer B.
Fundamenta Informaticae
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1999
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Vol. 37, Nr 3
225-246
EN
Linear Logic has been shown to incorporate a fragment suitable for representing P/T-nets and giving a semantics to the computations of such nets. This result is generalized to coloured nets. Furthermore a new kind of high-level nets is defined: Linear Logic Petri Nets (LLPN). These nets are used as an intuitive semantics to well-known and new high-level net concepts like object systems and agent orientation.
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