The removal of ε-transitions in weighted automata leads to infinite summation when cycles of such transitions are allowed. This paper presents both an algorithm for that purpose, and a framework in which the algorithm is correct.

We present a new proof of PSPACE-hardness of the emptiness problem for alternating finite automata with a singleton alphabet. This result was shown by Holzer (1995) who used a proof relying on a series of reductions from several papers. The new proof is simple, direct and self-contained.

Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve recognizability, ge...

In this paper, we have introduced the deterministic variant of parallel communicating Watson-Crick automata systems. We show that similar to the non-deterministic version, the deterministic version can also recognise some non-regular uniletter languages. We further establish that strongly deterministic Watson-Crick automata systems and deterministic Watson-Crick automata system are incomparable...

We construct automata over a binary alphabet with 2n states, n ≥ 2, whose states freely generate a free group of rank 2n. Combined with previous work, this shows that a free group of every finite rank can be generated by finite automata over a binary alphabet. We also construct free products of cyclic groups of order two via such automata.

We present finite automata for shuffle languages, iteration lemmata for languages with catenation and shuffle, closure properties of such language classes, as well as decidability results.

The large amount of information which has to be processed in the area of biology requires automated tools. Our work aims at creating a platform for the acquisition of gene functions from biological documents. The first step of our work consists in fitting an existing data-processing platform to this purpose.

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We show how weighted finite automata define topologies on the set of all ω-words over a finite alphabet X . Moreover, we give a characterization of these topologies in terms of topologies on Xω induces by languages U ⊆ X∗.