Static Watson-Crick Linear Grammars and Its Computational Power

Molecular computing has gained many interests among researchers since Head introduced the first theoretical model for DNA based computation using the splicing operation in 1987. Another model for DNA computing was proposed by using the sticker operation which Adlemanused in his successful experiment for the computation of Hamiltonian paths in a graph: a double stranded DNA sequence is composed by prolonging to the left and to the right a sequence of (single or double) symbols by using given single stranded strings or even more complex dominoes with sticky ends, gluing these ends together with the sticky ends of the current sequence according to a complementarity relation. According to this sticker operation, a language generative mechanism, called a sticker system, can be defined: a set of (incomplete) double-stranded sequences (axioms) and a set of pairs of single or double-stranded complementary sequences are given. The initial sequences are prolonged to the left and to the right by using sequences from the latter set, respectively. The iterations of these prolongations produce “computations” of possibly arbitrary length. These processes stop when a complete double stranded sequence is obtained. Sticker systems will generate only regular languages without restrictions. Additional restrictions can be imposed on the matching pairs of strands to obtain more powerful languages. Several types of sticker systems are shown to have the same power as regular grammars; one type is found to represent all linear languages whereas another one is proved to be able to represent any recursively enumerable language. The main aim of this research is to introduce and study sticker systems over monoids in which with each sticker operation, an element of a monoid is associated and a complete double stranded sequence is considered to be valid if the computation of the associated elements of the monoid produces the neutral element. Moreover, the sticker system over monoids is defined in this study.

Sticker systems

DNA computing is an area of natural computing based on the idea that molecular biology processes can be used to perform arithmetic and logic operations on information encoded as DNA strands. The first part of this review outlines basic molecular biology notions necessary for understanding DNA computing, recounts the first experimental demonstration of DNA computing (Adleman’s 7-vertex Hamiltonian Path Problem), and recounts the milestone wet laboratory experiment that first demonstrated the potential of DNA computing to outperform the computational ability of an unaided human (20 variable instance of 3-SAT).The second part of the review describes how the properties of DNA-based information, and in particular the Watson–Crick complementarity of DNA single strands, have influenced areas of theoretical computer science such as formal language theory, coding theory, automata theory and combinatorics on words. More precisely, we describe the problem of DNA encodings design, present an analysis of intramolecular bonds, define and characterize languages that avoid certain undesirable intermolecular bonds, and investigate languages whose words avoid even imperfect bindings between their constituent strands. We also present another, vectorial, representation of DNA strands, and two computational models based on this representation: sticker systems and Watson–Crick automata. Lastly, we describe the influence that properties of DNA-based information have had on research in combinatorics on words, by enumerating several natural generalizations of classical concepts of combinatorics of words: pseudopalindromes, pseudoperiodicity, Watson–Crick conjugate and commutative words, involutively bordered words, pseudoknot bordered words. In addition, we outline natural extensions in this context of two of the most fundamental results in combinatorics of words, namely Fine and Wilf's theorem and the Lyndon–Schutzenberger result.

We use random context picture grammars to generate pictures through successive refinement. The productions of such a grammar are context-free, but their application is regulated — "permitted" or "forbidden" — by context randomly distributed in the developing picture. Grammars using this relatively weak context often succeed where context-free grammars fail, e.g. in generating the Sierpiński carpets. On the other hand it proved possible to develop iteration theorems for three subclasses of these grammars, namely a pumping–shrinking, a pumping and a shrinking lemma for context-free, random permitting and random forbidding context picture grammars, respectively. Finding necessary conditions is problematic in the case of most models of context-free grammars with context-sensing ability, since they consider a variable and its context as a finite connected array. We have already shown that context-free picture grammars are strictly weaker than both random permitting and random forbidding context picture grammars, also that random permitting context is strictly weaker than random context. We now show that grammars which use forbidding context only are strictly weaker than random context picture grammars.

We investigate the grammatical complexity of finite languages w.r.t. context-free grammars and variants thereof. For fixed alphabets, it is shown that both the minimal number of productions and the minimal size of a context-free grammar generating a finite language cannot be approximated within a factor of \(o(p^{1/6})\) and \(o(s^{1/7})\), respectively, unless Open image in new window . Here, p is the number of productions and s the size of the given grammar. Similar inapproximability results also hold for linear context-free and right-linear (or regular) grammars. As a byproduct, we show that the language of all cubes of a given length requires an exponential number of context-free productions and we also investigate upper and lower bounds on the complexity of the operations union and concatenation for finite languages.

Despite early interest Predicate Invention has lately been under-explored within ILP. We develop a framework in which predicate invention and recursive generalisations are implemented using abduction with respect to a meta-interpreter. The approach is based on a previously unexplored case of Inverse Entailment for Grammatical Inference of Regular languages. Every abduced grammar H is represented by a conjunction of existentially quantified atomic formulae. Thus ¬H is a universally quantified clause representing a denial. The hypothesis space of solutions for ¬H can be ordered by ?-subsumption. We show that the representation can be mapped to a fragment of Higher-Order Datalog in which atomic formulae in H are projections of first-order definite clause grammar rules and the existentially quantified variables are projections of first-order predicate symbols. This allows predicate invention to be effected by the introduction of first-order variables. Previous work by Inoue and Furukawa used abduction and meta-level reasoning to invent predicates representing propositions. By contrast, the present paper uses abduction with a meta-interpretive framework to invent relations. We describe the implementations of Meta-interpretive Learning (MIL) using two different declarative representations: Prolog and Answer Set Programming (ASP). We compare these implementations against a state-of-the-art ILP system MC-TopLog using the dataset of learning Regular and Context-Free grammars as well learning a simplified natural language grammar and a grammatical description of a staircase. Experiments indicate that on randomly chosen grammars, the two implementations have significantly higher accuracies than MC-TopLog. In terms of running time, Metagol is overall fastest in these tasks. Experiments indicate that the Prolog implementation is competitive with the ASP one due to its ability to encode a strong procedural bias. We demonstrate that MIL can be applied to learning natural grammars. In this case experiments indicate that increasing the available background knowledge, reduces the running time. Additionally ASPM (ASP using a meta-interpreter) is shown to have a speed advantage over Metagol when background knowledge is sparse. We also demonstrate that by combining MetagolR (Metagol with a Regular grammar meta-interpreter) and MetagolCF (Context-Free meta-interpreter) we can formulate a system, MetagolRCF, which can change representation by firstly assuming the target to be Regular, and then failing this, switch to assuming it to be Context-Free. MetagolRCF runs up to 100 times faster than MetagolCF on grammars chosen randomly from Regular and non-Regular Context-Free grammars.

This paper defines the right‐longer (left‐longer) linear grammars with the property for every production rule as natural variants of even linear grammars definedThe relation is investigated among the language classes generated by those grammars, regular grammars, and linear context‐free grammars. Also investigated are the closure properties under some basic set operations.Finally, new homomorphic characterizations are given as follows. For every recursively enumerable language L, we can find two languages L1, L2 from each pair of those language classes except a pair of even linear languages and a homomorphism h such that L=h(L1L2). For the remainder pair, a result that h(L1L2) is linear context‐free is obtained.

This paper addresses two main aspects of DNA computing research: DNA computing in vitro and in vivo. We first present a model of DNA computation developed in [5]: the circular insertion/deletion system. We review the result obtained in [5] stating that this system has the computational power of a Turing machine, and present the outcome of a molecular biologylab oratoryex periment from [5] that implements a small instance of such a system. This shows that rewriting systems of the circular insertion/deletion type are viable alternatives in DNA computation in vitro. In the second half of the paper we address DNA computing in vivo by presenting a model proposed in [17] and developed in [18] for the homologous recombinations that take place during gene rearrangement in ciliates. Such a model has universal computational power which indicates that, in principle, some unicellular organisms may have the capacity to perform any computation carried out by an electronic computer.KeywordsTuring MachineFormal LanguageCircular StringDeletion RuleIntramolecular RecombinationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We have successfully designed and realized a common syntax-directed editing system, CSES. CSES can set up a syntax-directed editing system for the high level programming language described by context-free grammars and regular grammars. Syntax-directed, text editing and language recognizing technology combine perfectly in CSES. The paper expounds the theoretical basis, components, functions and prototype design of CSES, and briefly introduces the approaches and steps showing how to set up the syntax-directed editing system of the given language on CSES.

2 - State of the art: grammatical inference

In this thesis, various artificial recurrent neural network models are investigated for the problem of deriving grammar rules from a finite set of example sentences. A general discrete network framework and its corresponding learning algorithm are presented and studied in detail in learning three different types of grammars. The first type of grammars considered is regular grammars. Experiments with conventional analog recurrent networks in learning regular grammars are presented to demonstrate the unstable behavior of such networks in processing very long strings after training. A new network structure to force recurrent networks to learn stable states by discretizing the internal feedback signals is constructed. For training such discrete networks a learning rule is applied. As an extension to the discrete network model, an external discrete stack is added to accommodate the inference of context-free grammars. A composite error function is devised to deal with various situations during learning. The pseudo-gradient method is also extended to train such a network to learn context-free grammars with the added option of operating on the external stack. Another extension to the discrete network structure is made for the purpose of learning probabilistic finite state grammars. The network consists of a discrete portion which is intended to represent the structure of the grammar, and an analog portion which is intended to represent the transition probabilities. Two criteria for the network to verify the correctness of its solution during training are proposed. Theoretical analysis of the necessary and sufficient conditions for the correct solution is presented. Experimental results show that the discrete network models have similar capabilities in learning various grammars as their analog counterparts, and have the advantage of being provably stable.

In this last chapter we consider some more classes of machines and languages, besides those we have studied in the previous chapters. We also present some additional properties of finite automata, regular grammars, context-free grammars, and the so called abstract classes of languages. Finally, we present the Bernstein Theorem and we prove the existence of functions that are not computable.

RNA secondary structure prediction is a fundamental problem in bioinformatics. This paper proposes a new approach to predict RNA secondary structure based on Bayesian network. Compared to the existing sophisticated prediction approaches such as Zuker's algorithm and the stochastic context-free grammar (SCFG) model, Bayesian network can naturally incorporate a priori knowledge from different models sources, and moreover, they have great expression capabilities. Our approach provides an effective method of combining free energy information of Zuker algorithm with statistical information from SCFG probability model. Basically, the proposed approach is suitable to all kinds of existing SCFG grammar models. Taking the BJK grammar model as an example, this paper gives a complete description of our prediction algorithm. When performing on RNA datasets with known structures, the experimental results show that the prediction accuracy is considerably improved. The sensitivity and the correlation coefficient are increased by 7.91% and 5.70%, respectively, compared to the SCFG approach alone.

We analyze the complexity of membership problem for two subclasses of permutation languages: PermReg and PermLin. These are languages generated by regular and linear grammars respectively, extended by rules that allow to permute symbols in derivation, such as \(abX\rightarrow bXa\). We prove two NP-hardness results and analyze parameterized complexity of the problem.

While context-free grammars (CFGs) remain as one of the most important formalisms for interpreting natural language, word n-gram models are surprisingly powerful for domain-independent applications. We propose to unify these two formalisms for both speech recognition and spoken language understanding (SLU). With portability as the major problem, we incorporated domain-specific CFGs into a domain-independent n-gram model that can improve the generalizability of the CFG and the specificity of the n-gram. In our experiments, the unified model can significantly reduce the test set perplexity from 378 to 90 in comparison with a domain-independent word trigram. The unified model converges well when domain-specific data becomes available. The perplexity can be further reduced from 90 to 65 with a limited amount of domain-specific data. While we have demonstrated excellent portability, the full potential of our approach lies in its unified recognition and understanding that we are investigating.