Corpus ID: 49657067

Equivalence checking for weak bi-Kleene algebra

@article{Kapp2018EquivalenceCF,
  title={Equivalence checking for weak bi-Kleene algebra},
  author={Tobias Kapp{\'e} and Paul Brunet and B. Luttik and Alexandra Silva and F. Zanasi},
  journal={ArXiv},
  year={2018},
  volume={abs/1807.02102}
}
Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for language equivalence. Furthermore, we prove that this fragment corresponds precisely to series-rational expressions, i.e., rational expressions with an additional operator for bounded parallelism. As… Expand
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References

SHOWING 1-10 OF 46 REFERENCES
On Series-Parallel Pomset Languages: Rationality, Context-Freeness and Automata
TLDR
This paper precisely relates bi-Kleene Algebra (BKA), a fragment of CKA, to a novel type of automata, pomset automata (PAs), and shows that PAs can implement the BKA semantics of series-parallel rational expressions, and that a class of P as can be translated back to these expressions. Expand
On Decidability of Concurrent Kleene Algebra
TLDR
Constructions on Petri nets are used to provide two decision procedures for such pomset languages motivated by the equational and the refinement theory of concurrent Kleene algebra, which lies in a much simpler algorithm and an ExpSpace complexity bound. Expand
Concurrent Kleene Algebra
TLDR
A concurrent Kleene algebra is shown applicability of the algebra to a partially-ordered trace model of program execution semantics and its usefulness is demonstrated by validating familiar proof rules for sequential programs and for concurrent ones. Expand
Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages
TLDR
A new automaton model and a Kleene-like theorem are presented that relates a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. Expand
Completeness Theorems for Bi-Kleene Algebras and Series-Parallel Rational Pomset Languages
The congruence on series-parallel rational pomset expressions induced by series-parallel rational pomset language identity is shown to be axiomatised by the Kleene algebra axioms plus those ofExpand
Concurrent Kleene Algebra: Free Model and Completeness
TLDR
It is proved that the axioms for CKA with bounded parallelism are complete for the semantics proposed in the original paper; consequently, these semantics are the free model for this fragment of CKA. Expand
Concurrent Kleene algebra with tests and branching automata
TLDR
This work generalizes guarded strings to guarded series-parallel strings, or gsp-strings, to give a concrete language model for CKAT, and defines concurrent deterministic flowchart schemas and relate them to branching automata and to concurrent Kleene algebras with tests. Expand
Expressiveness modulo bisimilarity of regular expressions with parallel composition
TLDR
It is proved that the theory of regular expressions with ACP-style parallel composition and encapsulation is expressive enough to express all finite automata up to bisimilarity and extended the expressiveness results obtained by Bergstra, Bethke and Ponse are extended. Expand
A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events
  • D. Kozen
  • Computer Science, Mathematics
  • Inf. Comput.
  • 1994
A finitary axiomatization of the algebra of regular events involving only equations and equational implications that is sound for all interpretations over Kleene algebras is given. Axioms for KleeneExpand
Series-parallel languages and the bounded-width property
TLDR
The algebraic properties of the set of series–parallel posets are used to investigate the notion of recognizability, based on finite-index congruences, and a notion of regularity based on a new class of “branching” automata. Expand
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