Middle quotients of linear languages

Abstract

For two languagesX and Y, the middle quotient of X with respect to Y is denoted by and defined as and . In addition, if coincides with where and u is the reversal of v}, then is a stable middle quotient, denoted by . This paper proves that for every recursively enumerable language and , where A B C, and D are a linear language, a deterministic linear binary language, a linear language, and a minimal deterministic linear ternary language, respectively. Consequently and hold, too

Keywords:

• Recursively enumerable languages
• linear languages
• language operations
• middle quotients