Topological rewriting systems applied to standard bases and syntactic algebras

Autor: Cyrille Chenavier
Přispěvatelé: Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189 (CRIStAL), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Ecole Centrale de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Ecole Centrale de Lille, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2020
Předmět:
FOS: Computer and information sciences
Computer Science - Symbolic Computation
standard bases
Duality (mathematics)
Topological space
Symbolic Computation (cs.SC)
Topology
topological confluence
01 natural sciences
Computer Science::Logic in Computer Science
0103 physical sciences
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
FOS: Mathematics
series representations and syntactic algebras
0101 mathematics
Mathematics
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]
Algebra and Number Theory
Series (mathematics)
Formal power series
Discrete space
010102 general mathematics
68Q42 Secondary: 03G10
[MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA]
Mathematics - Rings and Algebras
series representations and syntactic algebras MSC 2010 -Primary: 13F25
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
Rings and Algebras (math.RA)
Confluence
TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS
Computer Science::Programming Languages
010307 mathematical physics
Rewriting
Reduction (mathematics)
Zdroj: Journal of Algebra
Journal of Algebra, Elsevier, In press, 550, pp.410-431. ⟨10.1016/j.jalgebra.2019.12.007⟩
Journal of Algebra, In press, 550, pp.410-431. ⟨10.1016/j.jalgebra.2019.12.007⟩
ISSN: 0021-8693
1090-266X
DOI: 10.1016/j.jalgebra.2019.12.007⟩
Popis: International audience; We introduce topological rewriting systems as a generalisation of abstract rewriting systems, where we replace the set of terms by a topological space. Abstract rewriting systems correspond to topological rewriting systems for the discrete topology. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting systems with continuous reduction operators, we show that the topological confluence property is characterised by lattice operations. Using this characterisation, we show that standard bases induce topologically confluent rewriting systems on formal power series. Finally, we investigate duality for reduction operators that we relate to series representations and syntactic algebras. In particular, we use duality for proving that an algebra is syntactic or not.
Databáze: OpenAIRE
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