32287187
Sticker systems with complex structures
Abstract In this paper, we propose a variant of sticker systems which uses molecules with complex structures. Since the original sticker systems (Paun et al. (1998) [2, 8]) working on double strands of DNA have been studied as a formal model for self-assembly in DNA computing, we extend the sticker systems to working on more complex (higher-order) structures of DNA molecules. The advantage of sticker systems with complex structures is that augmented with weak codings we can obtain the characterization of recursively enumerable languages by using only sticking (hybridization) operations for complex molecules, while the usual sticker systems require more complicated operations such as the simultaneous use of couples of dominoes or coherent computations besides morphisms.
60466000
The power of sequence design in DNA computing
Sequence design is a crucial problem in DNA-based computation. We introduce a simple strategy called Template method, which can systematically generate a set of sequences such that any sequence will have at least 4 mismatches with other sequences and with the concatenated part of other sequences.
26602421
Learning Approximately Regular Languages with Reversible Languages
In this note, we consider the problem of learning approximately regular languages in the limit from positive data using the class of k-reversible languages. The class of k-reversible languages was introduced by Angluin (1982), and proved to be efficiently identifiable in the limit from positive data only. We show that Angluin's learning algorithm for the class of k-reversible languages can be readily adopted for the approximate identification of regular languages from positive data. Considering the negative result on the exact identifiability by Gold (1967), this approximation approach would be one of the best we could hope for learning the class of regular languages from positive data only.
24210038
Necessary and sufficient conditions for learning with correction queries
We investigate the newly introduced model of learning with correction queries in the context of query learning. We present necessary and sufficient conditions for a class of languages to be inferable within this setting. We also offer a complete picture of how is the model of learning with corrections related with other well-established learning models, like the model of learning in the limit from positive data, or the one of learning with membership queries. As an application, we show that the class of k-reversible languages is learnable with correction queries.
16900268
On the Universality of Post and Splicing Systems
In search for a universal splicing system, in this paper we present a Post system universal for the class of Post systems, and we discuss its translation into an extended splicing system with multiplicity. We also discuss the complexity of the resulting universal splicing system, comparing our result with recent known results about the translation of universal Turing machines into splicing systems.
31006674
Identifiability of Subspaces and Homomorphic Images of Zero-Reversible Languages
In this paper, we study two operations of taking subspaces and homomorphic images of identifiable concept classes from positive data. We give sufficient conditions for the identifiable classes to be identifiable from positive data after the applications of those two operations. As one of the examples to show the effectiveness of the obtained theorems, we will apply them to the class of zero-reversible languages, and obtain some interesting identifiable language classes related to reversible languages. Further, we will show a connection of those theories to the theory of approximate identification in the limit from positive data([Kob96]). Another important contribution of this paper is an algebraic extension of Angluin's theorem in [Ang80] based on an algebraic characterization of zero-reversible languages given by [Pin87]. This generalized theorem tells us the importance of Pin's characterization of zero-reversible languages using finitely generated groups in the context of identification in the limit from positive data.
8742017
Two Extensions of PX system
Abstract Two extensions of PX system will be discussed. The extensions are ctPX (catch/throw PX) and mvPX (multiple values PX). ctPX is a PX system extended with Nakano's catch/throw logic. ctPX enables to extract LISP programs with catch/throw mechanism form natural proofs. mvPX is a PX system which uses multiple values rather than lists to keep a finite sequences of data. Programs extracted by ctPX are more efficient than the ones by the original PX.