Finite codes over free binoids

Authors:
Kosaburo Hashiguchi;Takahiro Kunai;Shuji Jimbo
Affiliations:
Department of Information Technology, Faculty of Engineering, Okayama University, Tsushima, Okayanma, 700-0082, Japan;Department of Information Technology, Faculty of Engineering, Tsushima, Okayama, 700-0082, Japan;Department of Information Technology, Faculty of Engineering, Tsushima, Okayama, 700-0082, Japan
Venue:
Journal of Automata, Languages and Combinatorics - Third international workshop on descriptional complexity of automata, grammars and related structures
Year:
2002

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Abstract

A binoid is an algebra which has two associative operations and the same identity to both operations. For any finite alphabet Σ, Σ*(^, •) denotes the free binoid generated by Σ with two independent associative operations ^ and • and the identity λ. We introduce the notion of two types of finite codes (^-codes and •-codes) over free binoids and show that for any given finite subset X of Σ*(^, •) and x ∈ [^, •], one can decide effectively whether X is a x-code or not.