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}
}
  • K. Lodaya, P. Weil
  • Published in STACS 25 February 1998
  • Mathematics, Computer Science
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… 
A Kleene Iteration for Parallelism
TLDR
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
  • P. Weil
  • 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
Series-Parallel Languages on Scattered and Countable Posets
TLDR
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
TLDR
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.
Series and Parallel Operations on Pomsets
TLDR
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
TLDR
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
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
  • Nicolas Bedon
  • Mathematics, Computer Science
    Log. Methods Comput. Sci.
  • 2015
TLDR
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.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 14 REFERENCES
Finite automata, their algebras and grammars - towards a theory of formal expressions
TLDR
This chapter discusses the structure Theory of Transition Algebras, the Structure and Behavior of Finite Automata, and General Alphabets: The Theory of Push-down Automata and Context-free Languages.
The Equational Theory of Pomsets
Full Abstraction for Series-Parallel Pomsets
  • L. Aceto
  • Mathematics, Computer Science
    TAPSOFT, Vol.1
  • 1991
TLDR
This paper shows that this simple model based on partial orders is fully-abstract with respect to the behavioural equivalence obtained by applying Abramsky's testing scenario for bisimulation equivalence in all refinement contexts, and provides a complete axiomatization of ST-trace equivalence over the class of series-parallel pomsets.
Graph Rewriting: An Algebraic and Logic Approach
  • B. Courcelle
  • Computer Science
    Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
  • 1990
Free Shuffle Algebras in Language Varieties
The Book of Traces
TLDR
This monograph covers all important research lines of the theory of traces and is organized in such a way that each chapter can be read independently - and hence is suitable for advanced courses/seminars on formal language theory and the Theory of concurrent systems.
Concurrency and Atomicity
The recognition of Series Parallel digraphs
TLDR
An algorithm is presented that recognizes the class of General Series Parallel digraphs and runs in time proportional to the size of its input and calculates the transitive reduction and transitive closure of any General Series parallel digraph.
Petri Nets: An Introduction
  • Wolfgang Reisig
  • Computer Science
    EATCS Monographs on Theoretical Computer Science
  • 1985
TLDR
The author presents an example for Applying S-Invariants: The Verification of Facts in C/E-Systems by Means of S- Invariants, a model based on the successful implementation of Nets Analysis in the context of Logic Circuits and Operating Systems.
A Complete Inference System for a Class of Regular Behaviours
  • R. Milner
  • Mathematics, Computer Science
    J. Comput. Syst. Sci.
  • 1984
...
1
2
...