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Properties of Super-Dual Nets

100%

Köhler M. , Rölke H.

Fundamenta Informaticae

2006

tom Vol. 72, nr 1-3

245-254

Petri nets can be dualised by interchanging the role of places and transitions. This notion of duality is applicable only for unmarked Petri nets, since a marked place would be translated to a marked transition - which is meaningless - in the dual net. In this presentation we study the formalism of super-dual nets which are a generalisation of Petri nets. Super-dual nets allow for marked transitions also. The properties and the relation to other net formalism is studied.

Concurrency in Mobile Object Net Systems

100%

Köhler M. , Rölke H.

Fundamenta Informaticae

2003

tom Vol. 54, nr 2,3

221-235

In this work we present the model of ``mobile object net systems'' - an algebraic formalisation of the ``nets within nets''-paradigm. The formalism of ``mobile object nets'' is well suited to express the dynamics of open, mobile systems, since it allows tokens to be active. The algebraic theory of ``mobile object net systems'' covers an integrated view of the two major topics concurrency and locality, which are central in the area of mobile computing. As a main result of this contribution, we derive an algebraic model in the ``Petri nets are monoids'' style. It is shown, that mobile object net systems are a conservative extension of the Petri net formalism.

Concurrent Turing Machines

80%

Farwer B. , Kudlek M. , Rölke H.

Fundamenta Informaticae

2007

tom Vol. 79, nr 3-4

303-317

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.

Petri Net Controlled Finite Automata

70%

Farwer B. , Jantzen M. , Kudlek M. , Rölke H. , Zetzsche G.

Fundamenta Informaticae

2008

tom Vol. 85, nr 1-4

111-121

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.