On regular languages over power sets

On regular languages over power sets

The power set of a finite set is used as the alphabet of a string interpreting a sentence of Monadic Second-Order Logic so that the string can be reduced (in straightforward ways) to the symbols occurring in the sentence. Simple extensions to regular expressions are described matching the succinctness of Monadic Second-Order Logic. A link to Goguen and Burstall's notion of an institution is for...

On the Acceptance Power of Regular Languages

Hertrampf et al. (1993) looked at complexity classes which are characterized (say accepted) by a regular language for the words of output bits produced by nondeterministic polynomial-time computations. A number of well-known complexity classes between P and PSPACE are accepted by regular languages. For example, NP is accepted by the regular language which consists of the words which contain at ...

Towards regular languages over in nite alphabets

Querying Regular Languages over Sliding Windows

We study the space complexity of querying regular languages over data streams in the sliding window model. The algorithm has to answer at any point of time whether the content of the sliding window belongs to a fixed regular language. A trichotomy is shown: For every regular language the optimal space requirement is either in Θ(n), Θ(logn), or constant, where n is the size of the sliding window...

Towards Regular Languages over Infinite Alphabets

Motivated by formal models recently proposed in the context of XML, we study automata and logics on strings over infinite alphabets. These are conservative extensions of classical automata and logics defining the regular languages on finite alphabets. Specifically, we consider register and pebble automata, and extensions of first-order logic and monadic second-order logic. For each type of auto...