Complex and complex-like traces

Volker Diekert

Abstract:
  
The definition and some known results on complex traces are
reviewed. We also discuss some open questions concerning the
Poset-property of complex traces.  The main new contribution of the
paper is the presentation of the notion of complex-like trace. Every
complex trace is complex-like, but there are other objects such as a
finite trace with some additional non-empty alphabetic information. In
the sequential case this information is nothing else than explicit
termination.Together with concurrency the concept leads to a rich
mathematical structure. Our results show that complex-like traces form
a prime algebraic and coherently complete Scott-domain. Our main
theorem shows that the concatenation on this domain is continuous.

@inproceedings{die93mfcs,
   author = "Diekert, V.",
   address = A-SPRINGER,
   booktitle = Pot # "18th Mathematical Foundations of Computer
            Science (MFCS~93), Gdansk (Polen) 1993",
   editor = "A. Borzyszkowski et al.",
   note = "Invited Lecture",
   number = "711",
   pages = "68-82",
   publisher = SPRINGER,
   series = LNCS,
   title = "Complex and complex-like traces",
   year = "1993",
   annote = "Dependence alphabets where the set of 
complex traces with prefix ordering forms a Scott domain
are characterized as cographs. 
The notion of complex-like fuzzy trace is introduced."
}