Automata and Concurrency

Abstract The purpose of this paper is twofold: to give a precise notion of a realization for simulation of one concurrent system by another, and to study the relations of modular concurrent systems and non-persistent (i.e. with conflicts) concurrent systems in an automatatheoretical style. We will introduce a conception of realization that obeys three requirements: - it allows for proper hierarchies in certain classes of concurrent systems, - it allows for normal-form theorems, and the standard constructions of the literature remain realizations in our formal concept, - it clarifies some counter-intuitive examples. Further, although our realization conception is developed to translate the computational aspects of concurrent systems, it also gives a formal tool for the handling of synchronization problems. The investigated concept of APA-nets (asynchronous, parallel automata nets) is by definition a modular system of networks of (finite state) machines and seems to be quite reasonable for modelling asynchronous, distributed systems. This modular approach is in some contrast to the non-persistency of Petri-nets, as in APA-nets conflicts may arise only as some non-determinism within components of the nets but not in the structure of the nets. As a bv-product we also investigate the relation of conflicts and non-determinism in concurrent systems.

[1]  George J. Klir,et al.  Applied General Systems Research , 1978 .

[2]  Hans Kleine Büning,et al.  Kleine universelle mehrdimensionale Turingmaschinen , 1977, J. Inf. Process. Cybern..

[3]  John L. Bruno,et al.  A Theory of Asynchronous Control Networks , 1971, IEEE Transactions on Computers.

[4]  T. Ottmann,et al.  Arithmetische Prädikate über einem Bereich endlicher Automaten , 1974 .

[5]  Kurt Jensen,et al.  A Method to Compare the Descriptive Power of Different Types of Petri Nets , 1980, MFCS.

[6]  Rüdiger Valk,et al.  Reductions of Nets and Parallel Prgrams , 1979, Advanced Course: Net Theory and Applications.

[7]  Suhas S. Patil,et al.  COORDINATION OF ASYNCHRONOUS EVENTS , 1970 .

[8]  M. Hack,et al.  PETRI NET LANGUAGE , 1976 .

[9]  Lutz Priese,et al.  Reversible Automaten und Einfache Universelle 2-Dimensionale Thue-Systeme , 1976, Math. Log. Q..

[10]  Y. S. Kwong,et al.  On Reduction of Asynchronous Systems , 1977, Theor. Comput. Sci..

[11]  Lutz Priese,et al.  Towards a Precise Characterization of the Complexity of Universal and Nonuniversal Turing Machines , 1979, SIAM J. Comput..

[12]  J. Hartmanis,et al.  Algebraic Structure Theory Of Sequential Machines , 1966 .

[13]  Jack B. Dennis,et al.  Programming generality, parallelism and computer architecture , 1968, IFIP Congress.

[14]  Robert M. Keller,et al.  Towards a Theory of Universal Speed-Independent Modules , 1974, IEEE Transactions on Computers.

[15]  B. K. Bhagavan,et al.  Fast Computational Algorithms for Bit Reversal , 1974, IEEE Transactions on Computers.

[16]  Walburga Rödding,et al.  On the aggregation of preferences , 1978 .

[17]  Thomas Ottmann,et al.  Über Möglichkeiten zur Simulation Endlicher Automaten durch eine Art Sequentieller Netzwerke aus einfachen Bausteinen , 1973 .

[18]  L. Priese.  Normed Networks: Their Mathematical Theory and Applicability , 1978 .

[19]  L. Priese,et al.  A Combinatorial Approach to Self-Correction , 1974 .

[20]  S. Rao Kosaraju,et al.  Limitations of Dijkstra's Semaphore Primitives and Petri nets , 1973, SOSP '73.