# Series-Parallel Posets: Algebra, Automata and Languages

@inproceedings{Lodaya1998SeriesParallelPA, title={Series-Parallel Posets: Algebra, Automata and Languages}, author={Kamal Lodaya and Pascal Weil}, booktitle={STACS}, year={1998} }

In order to model concurrency, we extend automata theory from the usual word languages (sets of labelled linear orders) to sets of labelled series-parallel posets - or, equivalently, to sets of terms in an algebra with two product operations: sequential and parallel. We first consider languages of posets having bounded width, and characterize them using depth-nilpotent algebras. Next we introduce series-rational expressions, a natural generalization of the usual rational expressions, as well as…

## 60 Citations

A Kleene Iteration for Parallelism

- Computer Science, MathematicsFSTTCS
- 1998

Rational expressions are defined, a natural generalization of the usual ones over words, and a Kleene theorem connecting them to regular languages (accepted by finite branching automata) is proved, showing that recognizable languages are strictly weaker.

A Kleene Iteration for Parallelism 1

- Computer Science, Mathematics
- 1998

This paper extends automata-theoretic techniques to unbounded parallel behaviour, as seen for instance in Petri nets. Languages are deened to be sets of (labelled) series-parallel posets | or,…

Series-parallel languages on scattered and countable posets

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2011

Series-Parallel Languages on Scattered and Countable Posets

- Mathematics, Computer ScienceMFCS
- 2007

The class of labelled posets considered in this paper is the smallest containing letters, closed under finite parallel operation and sequential product indexed by all countable and scattered linear orderings, which establishes that those labelledPosets are precisely the N-free ones.

Infinite Series-Parallel Posets: Logic and Languages

- Computer ScienceICALP
- 2000

This work extends recent work by Lodaya and Weil on sets of finite series-parallel pomsets in two aspects: It relates their notion of series-rationality to logical concepts, and it generalizes the equivalence of recognizability and series- rationality to infinite series-pomsets.

Logic and rational languages of scattered and countable series-parallel posets

- MathematicsTheor. Comput. Sci.
- 2020

Series and Parallel Operations on Pomsets

- MathematicsFSTTCS
- 1999

Two-sorted algebras of pomsets equipped with the operations of series and parallel product and series and Parallel omega power possess a non-finitely based polynomial time decidable equational theory which can be axiomatized by an infinite set of simple equations.

Rationality in Algebras with a Series Operation

- Mathematics, Computer ScienceInf. Comput.
- 2001

The notion of rationality in algebras with a designated binary associative operation called the series operation, or the sequential product is considered, and it is shown that this expressive power equals that of algebraic recognizability.

Logic and Rational Languages of Scattered and Countable Series-Parallel Posets

- MathematicsLATA
- 2019

We show that an extension of MSO with Presburger arithmetic, named P-MSO, is as expressive as branching automata over scattered and countable N-free posets. As a consequence of the effectiveness of…

Logic and Branching Automata

- Mathematics, Computer ScienceLog. Methods Comput. Sci.
- 2015

This paper proves that the class of languages of finite N-free posets recognized by branching automata is closed under complementation, and defines a logic, named P-MSO, as it is a extension of monadic second-order logic with Presburger arithmetic, and shows that it is precisely as expressive as branching Automata.

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