The Kleene Equality for Graphs

Abstract : In order to generalize the Kleene theorem from the free monoid to richer algebraic structures, we consider the non deterministic acceptance by a finite automaton of subsets of vertices of a graph. The subsets accepted in such a way are the equational subsets of vertices of the graph in the sense of Mezei and Wright. We introduce the notion of deterministic acceptance by finite automaton. A graph satisfies the Kleene equality if the two acceptance modes are equivalent, and in this case, the equational subsets form a Boolean algebra. We establish that the infinite grid and the transition graphs of deterministic pushdown automata satisfy the Kleene equality and we present families of graphs in which the free product of graphs preserves the Kleene equality.
Document type :
Conference papers
Complete list of metadatas

https://hal-upec-upem.archives-ouvertes.fr/hal-00620173
Contributor : Arnaud Carayol <>
Submitted on : Tuesday, March 5, 2013 - 10:50:37 PM
Last modification on : Friday, July 13, 2018 - 4:00:04 PM
Long-term archiving on : Thursday, June 6, 2013 - 3:55:09 AM

File

Kleene.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Arnaud Carayol, Didier Caucal. The Kleene Equality for Graphs. 31st International Symposium on Mathematical Foundations of Computer Science (MFCS'06), Aug 2006, Stará Lesná, Slovakia. pp.214-225, ⟨10.1007/11821069_19⟩. ⟨hal-00620173⟩

Share

Metrics

Record views

358

Files downloads

79