Circular Languages Generated by Complete Splicing Systems and Pure Unitary Languages

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for complete systems, which are special finite circular splicing systems. We show that a circular language L is generated by a complete system if and only if the set Lin(L) of all words corresponding to L is a pure unitary language generated by a set closed under the conjugacy relation. The class of pure unitary languages was introduced by A. Ehrenfeucht, D. Haussler, G. Rozenberg in 1983, as a subclass of the class of context-free languages, together with a characterization of regular pure unitary languages by means of a decidable property. As a direct consequence, we characterize (regular) circular languages generated by complete systems. We can also decide whether the language generated by a complete system is regular. Finally, we point out that complete systems have the same computational power as finite simple systems, an easy type of circular splicing system defined in the literature from the very beginning, when only one rule is allowed. From our results on complete systems, it follows that finite simple systems generate a class of context-free languages containing non-regular languages, showing the incorrectness of a longstanding result on simple systems

A Picture Array Generating Model Based on Flat Splicing Operation

The bio-inspired operations of linear and circular splicing respectively on linear and circular strings of symbols have been extensively investigated by many researchers for their theoretical properties. Recently, another kind of splicing of two words, referred to as flat splicing on strings, has been considered. We here extend this operation to flat splicing on picture arrays, thus defining a new model of picture generation, which we call as array flat splicing system (AF S) and obtain some results on the generative power of AF S in comparison with certain well-known picture array defining model

Splicing Systems from Past to Future: Old and New Challenges

A splicing system is a formal model of a recombinant behaviour of sets of double stranded DNA molecules when acted on by restriction enzymes and ligase. In this survey we will concentrate on a specific behaviour of a type of splicing systems, introduced by P\u{a}un and subsequently developed by many researchers in both linear and circular case of splicing definition. In particular, we will present recent results on this topic and how they stimulate new challenging investigations.Comment: Appeared in: Discrete Mathematics and Computer Science. Papers in Memoriam Alexandru Mateescu (1952-2005). The Publishing House of the Romanian Academy, 2014. arXiv admin note: text overlap with arXiv:1112.4897 by other author

Influence of reflected radiation waves caused by large mode field and large refractive index mismatches on splice loss evaluation between elliptical-hole lattice core holey fibers and conventional fibers

When the mode field and refractive index mismatches between two spliced fibers are small, the splice loss is generally evaluated by calculating an overlap integral without reflection waves. A single-polarization circular-hole holey fiber with a core consisting of an elliptical-hole lattice (EC-CHF) has a strikingly different mode field caused by elliptical holes in the core region from those of conventional single-mode fibers (SMFs) and, thus, reflected radiation modes may significantly appear in splicing an EC-CHF to conventional SMFs. We study the influence of reflected radiation modes on the splice loss evaluation of optical fibers with large mode field and large refractive index mismatches through numerical analyses using a bidirectional eigenmode propagation method and a three-dimensional finite-element method

Language generating alphabetic flat splicing P systems

An operation on strings, called at splicing was introduced, inspired by a splicing operation on circular strings considered in the study of modelling of the recombinant behaviour of DNA molecules. A simple kind of at splicing, called alphabetic at splicing, allows insertion of a word with a specified start symbol and/or a specified end symbol, between two pre-determined symbols in a given word. In this work, we consider a P system with only alphabetic at splicing rules as the evolution rules and strings of symbols as objects in its regions. We examine the language generative power of the resulting alphabetic at splicing P systems (AFS P systems, for short). In particular, we show that AFS P systems with two membranes are more powerful in generative power than AFS P systems with a single membrane. We also construct AFS P systems with at most three membranes to generate languages that do not belong to certain other language classes and show an application to generation of chain code pictures

Stabilized large mode area in tapered photonic crystal fiber for stable coupling

A rigorous modal solution approach based on the numerically efficient finite element method (FEM) has been used to design a tapered photonic crystal fiber with a large mode area that could be efficiently coupled to an optical fiber. Here, for the first time, we report that the expanded mode area can be stabilized against possible fabrication tolerances by introducing a secondary surrounding waveguide with larger air holes in the outer ring. A full-vectorial -field approach is employed to obtain mode field areas along the tapered section, and the Least Squares Boundary Residual (LSBR) method is used to obtain the coupling coefficients to a butt-coupled fiber

A unified mechanism for intron and exon definition and back-splicing.

The molecular mechanisms of exon definition and back-splicing are fundamental unanswered questions in pre-mRNA splicing. Here we report cryo-electron microscopy structures of the yeast spliceosomal E complex assembled on introns, providing a view of the earliest event in the splicing cycle that commits pre-mRNAs to splicing. The E complex architecture suggests that the same spliceosome can assemble across an exon, and that it either remodels to span an intron for canonical linear splicing (typically on short exons) or catalyses back-splicing to generate circular RNA (on long exons). The model is supported by our experiments, which show that an E complex assembled on the middle exon of yeast EFM5 or HMRA1 can be chased into circular RNA when the exon is sufficiently long. This simple model unifies intron definition, exon definition, and back-splicing through the same spliceosome in all eukaryotes and should inspire experiments in many other systems to understand the mechanism and regulation of these processes