Symmetries of the Partial Order of Traces

This paper deals with the automorphism group of the partial order of finite traces. We show that any group can arise as such an automorphism group if we allow arbitrary large dependence alphabets. Restricting to finite dependence alphabets, the automorphism groups are profinite and possess only finitely many simple decomposition factors. Finally, we show that the partial order associated with the Rado graph as dependence alphabet does not give rise to a homogeneous domain thereby answering an open question from Boldi, P., Cardone, F. and Sabadini, N. (1993).

[1]  John K. Truss,et al.  The group of the countable universal graph , 1985, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  Manfred Droste,et al.  Universal Homogeneous Event Structures and Domains , 1991, Inf. Comput..

[3]  G. Sabidussi.  Graphs with given infinite group , 1960 .

[4]  Paul Gastin,et al.  Poset Properties of Complex Traces , 1992, MFCS.

[5]  P. Cameron.  Combinatorics: Topics, Techniques, Algorithms , 1995 .

[6]  R. Frucht.  Herstellung von Graphen mit vorgegebener abstrakter Gruppe , 1939 .

[7]  Pierre Cartier,et al.  Problemes combinatoires de commutation et rearrangements , 1969 .

[8]  Dietrich Kuske.  Nondeterministic Automata with Concurrency Relations and Domains , 1994, CAAP.

[9]  Manfred Droste.  Concurrent Automata and Domains , 1992, Int. J. Found. Comput. Sci..

[10]  Bruno Courcelle,et al.  Graph Rewriting: An Algebraic and Logic Approach , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[11]  A. Mazurkiewicz.  Concurrent Program Schemes and their Interpretations , 1977 .

[12]  Paul Gastin,et al.  Infinite Traces , 1990, Semantics of Systems of Concurrent Processes.

[13]  Marta Z. Kwiatkowska,et al.  On the Domain of Traces and Sequential Composition , 1991, TAPSOFT, Vol.1.

[14]  O. Ore.  Theory of Graphs , 1962 .

[15]  Paul Gastin,et al.  The Poset of Infinitary Traces , 1993, Theor. Comput. Sci..