A Formalization of Co-Transcriptional Splicing as an Operation on Formal Languages

RNA co-transcriptionality is the process where RNA sequences are spliced while being transcribed from DNA templates. This process holds potential as a key tool for molecular programming. Co-transcriptional folding has been shown to be programmable for assembling nano-scale RNA structures, and recent advances have proven its Turing universality. While post-transcriptional splicing has been extensively studied, co-transcriptional splicing is gaining attention for its potential to save resources and space in molecular systems. However, its unpredictability has limited its practical applications. In this paper, we focus on engineering co-transcriptional splicing, moving beyond natural occurrences to program RNA sequences that produce specific target sequences through DNA templates. We introduce contextual lariat deletion operations under three energy models - linear loop penalty, logarithmic loop penalty, and constantly bounded loop length - as well as bracketed contextual deletion, where deletion occurs solely based on context matching, without any structural constraints from hairpin loops. We examine the complexity of the template constructability problem associated with these operations and study the closure properties of the languages they generate, providing insights for RNA template design in molecular programming systems.