Modeling concurrency with partial orders
International Journal of Parallel Programming
The equational theory of pomsets
Theoretical Computer Science
Full abstraction for series-parallel pomsets
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
Towards action-refinement in process algebras
Information and Computation
Free shuffle algebras in language varieties
Theoretical Computer Science
Free Shuffle Algebras in Language Varieties (Extended Abstract)
LATIN '95 Proceedings of the Second Latin American Symposium on Theoretical Informatics
Partial orders and the axiomatic theory of shuffle (pomsets)
Partial orders and the axiomatic theory of shuffle (pomsets)
CCS with Hennessy's merge has no finite-equational axiomatization
Theoretical Computer Science - Expressiveness in concurrency
The saga of the axiomatization of parallel composition
CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory
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A V-labelled poset P can induce an operation on the languages on any fixed alphabet, as well as an operation on labelled posets (as noticed by Pratt and Gischer (Pratt 1986; Gischer 1988)). For any collection X of V-labelled posets and any alphabet Σ we obtain an X-algebra Σ X of languages on Σ. We consider the variety Lang(X) generated by these algebras when X is a collection of nonempty ‘traceable posets’. The current paper contains several observations about this variety. First, we use one of the basic results in Bloom and Ésik (1996) to show that a concrete description of the A-generated free algebra in Lang(X) is the X-subalgebra generated by the singletons (labelled a∈A) in the X-algebra of all A-labelled posets. Equipped with an appropriate ordering, these same algebras are the free ordered algebras in the variety Lang(X) ⩽ of ordered language X-algebras. Further, if one enriches the language algebras by adding either a binary or infinitary union operation, the free algebras in the resulting variety are described by certain ‘closed’ subsets of the original free algebras. Second, we show that for ‘reasonable sets’ X, the variety Lang(X) has the property that for each n⩾2, the n-generated free algebra is a subalgebra of the 1-generated free algebra. Third, knowing the free algebras enables us to show that these varieties are generated by the finite languages on a two-letter alphabet.