Affiliations: Institute for Theoretical Computer Science, Technical University of Dresden, Dresden D-01062, Germany. baader@tcs.inf.tu-dresden.de | Department of Mathematics and Statistics, University of Turku, Turku FI-20014, Finland. alexander.okhotin@utu.fi
Note: [] Address for correspondence: Institute for Theoretical Computer Science, Technical University of Dresden, Dresden D-01062, Germany
Note: [] Supported by the Academy of Finland under grants 134860 and 257857.
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.
