Takashi Yokomori

Spiking Neural P Systems

We bring together two topics recently introduced in membrane computing, the much investigated spiking neural P systems (in short, SN P systems), inspired from the way the neurons communicate through spikes, and the dP systems (distributed P systems, with components which “read” strings from the environment and then cooperate in accepting their concatenation). The goal is to introduce SN dP systems, and to this aim we first introduce SN P systems with the possibility to input, at their request, spikes from the environment; this is done by so-called request rules. A preliminary investigation of the obtained SN dP systems (they can also be called automata) is carried out. As expected, request rules are useful, while the distribution in terms of dP systems can handle languages which cannot be generated by usual SN P systems. We always work with extended SN P systems; the non-extended case, as well as several other natural questions remain open.

Tree adjoining grammars for RNA structure prediction

In this paper, we are concerned with identifying a subclass of tree adjoining grammars (TAGs) that is suitable for the application to modeling and predicting RNA secondary structures. The goal of this paper is twofold: For the purpose of applying to the RNA secondary structure prediction problem, we first introduce a special subclass of TAGs and develop a fast parsing algorithm for the subclass, together with some of its language theoretic characterizations. Then, based on the algorithm, we develop a prediction system and demonstrate the effectiveness of the system by presenting some experimental results obtained from biological data, where free energy evaluation selection for parse trees is incorporated into the algorithm.

Polynomial-time identification of very simple grammars from positive data

This paper concerns a subclass of simple deterministic grammars, called very simple grammars, and studies the problem of identifying the subclass in the limit from positive data. The class of very simple languages forms a proper subclass of simple deterministic languages and is incomparable to the class of regular languages. This class of languages is also known as the class of left Szilard languages of context-free grammars.After providing some properties of very simple languages, we show that the class of very simple grammars is polynomial-time identifiable in the limit from positive data in the following sense. That is, we show that there effectively exists an algorithm that, given a target very simple grammar G* over alphabet Σ, identifies a very simple grammar G equivalent to G* in the limit from positive data, satisfying the property that the time for updating a conjecture is bounded by O(m), and the total number of prediction errors made by the algorithm is bounded by O(n), where n is the size of G*, m = Max{N|Σ|+1, |Σ|3} and N is the total length of all positive data provided.

On the Computational Power of Insertion-Deletion Systems

Gene insertion and deletion are basic phenomena found in DNA processing or RNA editing in molecular biology. The genetic mechanism and development based on these evolutionary transformations have been formulated as a formal system with two operations of insertion and deletion, called insertion-deletion systems (Kari and Thierrin, 1996; Kari et al., 1997).We investigate the generative power of insertion-deletion systems (InsDel systems), and show that the family INS11DEL11 is equal to the family of recursively enumerable languages. This gives a positive answer to an open problem posed in Kari et al. (1997) where it was conjectured contrary.

On Polynomial-Time Learnability in the Limit of Strictly Deterministic Automata

This paper deals with the polynomial-time learnability of a language class in the limit from positive data, and discusses the learning problem of a subclass of deterministic finite automata (DFAs), called strictly deterministic automata (SDAs), in the framework of learning in the limit from positive data. We first discuss the difficulty of Pitts definition in the framework of learning in the limit from positive data, by showing that any class of languages with an infinite descending chain property is not polynomial-time learnable in the limit from positive data. We then propose new definitions for polynomial-time learnability in the limit from positive data. We show in our new definitions that the class of SDAs is iteratively, consistently polynomial-time learnable in the limit from positive data. In particular, we present a learning algorithm that learns any SDA M in the limit from positive data, satisfying the properties that (i) the time for updating a conjecture is at most O(lm), (ii) the number of implicit prediction errors is at most O(ln), where l is the maximum length of all positive data provided, m is the alphabet size of M and n is the size of M, (iii) each conjecture is computed from only the previous conjecture and the current example, and (iv) at any stage the conjecture is consistent with the sample set seen so far. This is in marked contrast to the fact that the class of DFAs is neither learnable in the limit from positive data nor polynomial-time learnable in the limit.

On the power of membrane division in P systems

First, we consider P systems with active membranes, hence with the possibility that the membranes can be divided, with non-cooperating evolution rules (the objects always evolve separately). These systems are known to be able to solve NP-complete problems in linear time. Here we give a normal form theorem for such systems: their computational universality is preserved even if only the elementary membranes are divided. The possibility of solving SAT in linear time is preserved only when non-elementary membranes may also be divided under the influence of objects in their region.Second, we consider a slight generalization, namely, we allow that a membrane can produce by division both a copy of itself and a copy of a membrane with a different label; again, only elementary membranes may be divided. In this case, we prove that the hierarchy on the maximal number of membranes present in the system collapses: three membranes at a time are sufficient in order to characterize the recursively enumerable sets of vectors of natural numbers. This result is optimal, two membranes are shown not to be sufficient.Third, we consider P systems with cooperating rules (several objects may evolve together). Making use of this powerful feature, we show that many NP-complete problems can be solved in linear time in a quite uniform way (by systems which are very similar to each other), using only elementary membranes division (and not further ingredients, such as electrical charges). The degree of cooperation is minimal: two objects at a time.

Two complementary operations inspired by the DNA hairpin formation: Completion and reduction

We consider two complementary operations: Hairpin completion introduced in [D. Cheptea, C. Martin-Vide, V. Mitrana, A new operation on words suggested by DNA biochemistry: Hairpin completion, in: Proc. Transgressive Computing, 2006, pp. 216-228] with motivations coming from DNA biochemistry and hairpin reduction as the inverse operation of the hairpin completion. Both operations are viewed here as formal operations on words and languages. We settle the closure properties of the classes of regular and linear context-free languages under hairpin completion in comparison with hairpin reduction. While the class of linear context-free languages is exactly the weak-code image of the class of the hairpin completion of regular languages, rather surprisingly, the weak-code image of the class of the hairpin completion of linear context-free languages is a class of mildly context-sensitive languages. The closure properties with respect to the hairpin reduction of some time and space complexity classes are also studied. We show that the factors found in the general cases are not necessary for regular and context-free languages. This part of the paper completes the results given in the earlier paper, where a similar investigation was made for hairpin completion. Finally, we briefly discuss the iterated variants of these operations.

Learning local languages and their application to DNA sequence analysis

This paper presents an efficient algorithm for learning in the limit a special type of regular languages, called strictly locally testable languages from positive data, and its application to identifying the protein /spl alpha/-chain region in amino acid sequences. First, we present a linear time algorithm that, given a strictly locally testable language, learns its deterministic finite state automaton in the limit from only positive data. This provides one with a practical and efficient method for learning a specific concept domain of sequence analysis. We then describe several experimental results using the learning algorithm developed above. Following a theoretical observation which strongly suggests that a certain type of amino acid sequences can be expressed by a locally testable language, we apply the learning algorithm to identifying the protein /spl alpha/-chain region in amino acid sequences for hemoglobin. Experimental scores show an overall success rate of 95% correct identification for positive data, and 96% for negative data.

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 Angluins 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.

On Approximately Identifying Concept Classes in the Limit

In this paper, we introduce various kinds of approximations of a concept and propose a framework of approximate learning in case that a target concept could be outside the hypothesis space. We present some characterization theorems for approximately identifiability. In particular, we show a remarkable result that the upper-best approximate identifiability from complete data is collapsed into the upper-best approximate identifiability from positive data. Further, some other characterizations for approximate identifiability from positive data are presented, where we establish a relationship between approximate identifiability and some important notions in quasi-order theory and topology theory. The results obtained in this paper are essentially related to the closure property of concept classes under infinite intersections (or infinite unions). We also show that there exist some interesting example concept classes with such properties (including specialized EFSs) by which an upper-best approximation of any concept can be identifiable in the limit from positive data.