Bioinformatics (2019) doi:http://dx.doi.org/10.1093/bioinformatics/bty922 In the originally published version of this manuscript, there was an error in the ‘Availability and implementation’ section of the Abstract. The URL for the browser tracks should be: guanine.evolbio.mpg.de/complexity This detail has been corrected only in this corrigendum to preserve the published version of record.

Determinization of Büchi automata is a long-known difficult problem, and after the seminal result of Safra, who developed the first asymptotically optimal construction from Büchi into Rabin automata, much work went into improving, simplifying, or avoiding Safra’s construction. A different, less known determinization construction was proposed by Muller and Schupp. The two types of constructions share some similarities but their precise relationship was still unclear. In this paper, we shed some light on this relationship by proposing a construction from nondeterministic Büchi to deterministic parity automata that subsumes both constructions: Our construction leaves some freedom in the choice of the successor states of the deterministic automaton, and by instantiating these choices in different ways, one obtains as particular cases the construction of Safra and the construction of Muller and Schupp. The basis is a correspondence between structures that are encoded in the macrostates of the determinization procedures - Safra trees on one hand, and levels of the split-tree, which underlies the Muller and Schupp construction, on the other hand. Our construction also allows for mixing the mentioned constructions, and opens up new directions for the development of heuristics.

MOTIVATION: Unique sequence regions are associated with genetic function in vertebrate genomes. However, measuring uniqueness, or absence of long repeats, along a genome is conceptually and computationally difficult. Here we use a variant of the Lempel-Ziv complexity, the match complexity, Cm, and augment it by deriving its null distribution for random sequences. We then apply Cm to the human and mouse genomes to investigate the relationship between sequence complexity and function. RESULTS: We implemented Cm in the program macle and show through simulation that the newly derived null distribution of Cm is accurate. This allows us to delineate high-complexity regions in the human and mouse genomes. Using our program macle2go, we find that these regions are twofold enriched for genes. Moreover, the genes contained in these regions are more than 10-fold enriched for developmental functions. AVAILABILITY AND IMPLEMENTATION: Source code for macle and macle2go is available from www.github.com/evolbioinf/macle and www.github.com/evolbioinf/macle2go, respectively; Cm browser tracks from guanine.evolbio.mgp.de/complexity. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.