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On Language Equations with One-sided Concatenation

100%

Baader F. , Okhotin A.

Fundamenta Informaticae

2013

tom Vol. 126, nr 1

1--35

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.

From Tableaux to Automata for Description Logics

80%

Baader F. , Hladik J. , Lutz C. , Wolter F.

Fundamenta Informaticae

2003

tom Vol. 57, nr 2-4

247--279

This paper investigates the relationship between automata- and tableau-based inference procedures for description logics. To be more precise, we develop an abstract notion of what a tableau-based algorithm is, and then show, on this abstract level, how tableau-based algorithms can be converted into automata-based algorithms. In particular, this allows us to characterize a large class of tableau-based algorithms that imply an ExpTime upper-bound for reasoning in the description logics for which such an algorithm exists.