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On Language Equations with One-Sided Concatenation

Franz Baader, Alexander Okhotin, On Language Equations with One-Sided Concatenation. TUCS Technical Reports 743, Turku Centre for Computer Science, 2006.

Abstract:

Language equations are equations where both the constants occurring in the equations and the solutions are formal languages. They have first been introduced in formal language theory, but are now also considered in other areas of computer science. In the present paper, we restrict the attention to language equations with one-sided concatenation, but in contrast to previous work on these equations, we allow not just union but all Boolean operations to be used when formulating them. In addition, we are not just interested in deciding solvability of such equations, but also in deciding other properties of the set of solutions, like its cardinality (finite, infinite, uncountable) and whether it contains least/greatest solutions. We show that all these decision problems are ExpTime-complete.

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BibTeX entry:

@TECHREPORT{tBaOk06a,
  title = {On Language Equations with One-Sided Concatenation},
  author = {Baader, Franz and Okhotin, Alexander},
  number = {743},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2006},
  keywords = {Language equations, tree automata, computational complexity},
  ISBN = {952-12-1686-7},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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