JUCS - Journal of Universal Computer Science 16(5): 653-675, doi: 10.3217/jucs-016-05-0653
Orthogonal Concatenation: Language Equations and State Complexity
expand article infoMark Daley‡, Michael Domaratzki§, Kai Salomaa|
‡ University of Western Ontario London, daley@csd.uwo.ca, Canada§ University of Manitoba Winnipeg, mdomarat@cs.umanitoba.ca, Canada| Queen's University, Kingston, Canada

Corresponding author: Mark Daley ( daley@csd.uwo.ca )

© Mark Daley, Michael Domaratzki, Kai Salomaa.
This article is freely available under the J.UCS Open Content License.
Citation: Daley M, Domaratzki M, Salomaa K (2010) Orthogonal Concatenation: Language Equations and State Complexity. JUCS - Journal of Universal Computer Science 16(5): 653-675. https://doi.org/10.3217/jucs-016-05-0653
Open Access
Abstract
A language L is the orthogonal concatenation of languages L1 and L2 if every word of L can be written in a unique way as a concatenation of a word in L1 and a word in L2. The notion can be generalized for arbitrary language operations. We consider decidability properties of language orthogonality and the solvability of language equations involving the orthogonal concatenation operation. We establish a tight bound for the state complexity of orthogonal concatenation of regular languages.
Keywords
language operations, language equations, regular languages, state complexity, decidability