### New Trends in Formal Languages: Control, Cooperation, and Combinatorics

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We may comprehend the basic dynamical properties of such networks. It can be shown, that in the dynamical systems defined this way the notions and means used in continuous dynamics find their paralell.

Networks of language processors NLP systems are unconventional models of computing, introduced for describing the behaviour of communities of dynamically changing and communicating agents in terms of formal grammars and languages. A network of language processors is a virtual graph with a language identifying mechanism a grammar, an automaton, etc.

### ICCGI 12222

These language processors work in a synchronized manner by performing rewriting steps and communication steps. At a rewriting step, each language processor rewrites the strings or some of them that can be found at that moment at the node, and then a communication step follows. At this step, the language processors, according to the communication protocol of the network, communicate the previously rewritten strings to the other nodes.

A sequence of alternating rewriting steps and communication steps determine a computation in the network. The result of the computation can be defined as the set or the multiset of words which can be found at a dedicated node under computation or at some previously fixed step of the computation. Networks of language processors are not only tools for computation determining languages but also can be used for studying questions as the description of the dynamics of string multisets at the nodes.

If the words are considered as descriptions of organisms or they identify DNA sequences, then NLP systems can be useful in describing the behaviour of interacting populations with dynamically changing members. In this talk we discuss two variants of NLP systems, networks of Lindenmayer systems and networks of Watson-Crick Lindenmayer systems, both demonstrating the power of this framework.

In the case of networks of Lindenmayer systems the component language processors are grammars with totally parallel rewriting, modelling developmental systems. In the case of Watson-Crick Lindenmayer systems the totally parallel rewriting the development is triggered by a fundamental property of DNA computing, the Watson-Crick complementarity.

We show that both models, even with very simple language processors and communication protocols, are as powerful as the Turing machines, moreover, for the massive parallelism some well-known NP-complete problems can be solved by these constructs in linear time. Finally, we demonstrate a method for describing the dynamics of the string multisets occurring under computation in these networks.

Linguistic Capacity: Associative or Combinatory? Chomskyan models of natural-language grammars, based on formal language theory, crucially rely on the assumption that linguistic knowledge contains two different components, namely, one combinatory system syntax and one that contains knowledge about the use of elementary building blocks lexicon. Post-Chomskyan theories of grammar in particular, Construction Grammar posits that words and syntactic structures and whatever is in between must be treated in a homogeneous manner, since they are all alike in that they consist in associations of formal properties with semantic ones.

In accordance with this, constructionism says we do not use linearly ordered sequences consisting of lexical building blocks in linguistic communication, but complex and possibly overlapping patterns constructions arising from the simultaneous satisfaction of various constraints. Mindmaker Ltd. In this implementation, constructions constitute a network, and they activate each other through associations. Yet, each carries essentially symbolic information, and the task is essentially combinatory.

It is unclear for the moment how familiar sub-symbolic representation and learning systems e. The long-awaited book of Stephen Wolfram has been completed. This massive, page tome is a great intellectual achievement: one of his friends suggested it should be called PrincipiaComputatus. Using the early results of his investigations into the behaviours of cellular automata, and the technical computing system Mathematica he created, the book presents a huge number of examples of various scientific disciplines where simple rules generate immensely complex results. The book culminates in the Principle of Computational Equivalence implying that at some level of complexity everything is exactly as complex as anything else.

A New Kind of Science is a readable book sharing his ideas with scientists and also with nonscientists. Throughout the book, emphasis is placed on the algorithm rather than the equation. Wolfram predicts it will have unprecedented implications for science and scientific thinking. Understanding the function of the prefrontal cortex PFC is crucial to reveal the biological mechanisms of thought— and mood disorders and it is also a central question in cognitive neuroscience.

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It is widely accepted that PFC plays essential role in working memory, especially in executive functions, a main component of working memory. From neurobiological perspective the function of working memory is maintaining neural representations of different kind of sensory or learned information temporally in activated form for on-line processing. Manipulation of this information held in working memory by executive functions is a necessary step to goal directed behavior.

A characteristic feature of neuronal activity in the PFC is the vigorous response in tasks requiring short term retention of information, like delay response tasks.

Disturbance of this activity results in faulty behavioral responses indicating its central role in normal functions as well as clinical symptoms. It is reasonable to assume that optimal regulation of delay-related activity is essential for flexible and at the same time accurate behavior. Accordingly, irresistible activity or instability of it could result in perseveration or distractibility, respectively, which are characteristic symptoms of prefrontal dysfunction. The original idea about the neuronal mechanisms underlying delay-related activity was that reverberation of activity between interconnected neurons.

However, this mechanistic proposal has a limited explanatory power considering the diversity of circuits integrated in the PFC. The purpose of this talk is to give an introduction about the state of our knowledge regarding on the organizational principles of these cortical and subcortical networks whose activities are needed to be integrated in a comprehensive model of the PFC.

An overview is given about the Neural Networks, the recently developed, but not yet released application of Mathematica. The most significant feature of this package, that the symbolic form of a trained network can be produced, consequently it is an easy job to implement it into other applications. Examples from different fields of sciences will demonstrate the usage of the different type of networks, which are available in the Neural Networks application.

Experiments have in number theory a long tradition, although they were called rather as examination of tables or numerical test of conjectures. Both Gauss and Riemann did thorough numerical investigations with "pencil on paper" before stating the conjectures. In the 20th century because of the idea of computers and the development of the algorithmic point of view more and more researcher were interested for the representation of mathematical objects and algorithmic aspects of operations.

The investigations of Derek and Emma Lehmer, Zassenhaus and Cassels means a transition from the precomputer to the computer age. They belong to those scientists, who realized that computers may become experimental facilities for mathematics. One of the most important results of the beginning, i. It was stated again after long and careful numerical tests, but this time the tests were done by computers.

The solution of diophantine equations is an interesting branch of number theory since ancient ages. A systematic theory exists only since the beginning of the 20th century, by our opinion since the talk of Hilbert at the 2nd Conference of Mathematicians in Paris, In Debrecen investigations started in this directions in the early 80th. We developed algorithms among others for the solution of Thue-, index form- and elliptic equations, implemented and applied them for large sets of input data. Our most important result was that such equations have usually only small solutions. Our numerical results influenced the theoretical investigations; the explicit determination and the size of constants are playing nowadays an important role and the proof of several theorems were simplified.

By the examination of the results one should be careful, because the usual answer is that the problem has only trivial solutions. The situation is similar to the primality tests. NDL India is a conglomeration of freely available or institutionally contributed or donated or publisher managed contents. Almost all these contents are hosted and accessed from respective sources.

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