Brains as naturally emerging turing machines

A language is called (m,n)-verbose if there exists a Turing machine that enumerates for any n words at most m possibilities for their characteristic string. This notion is compared with (m,n)-fa-verboseness, where instead of a Turing machine a finite automaton is used. By use of a new diagonalisation method, where finite automata trick Turing machines, it is shown that all (m,n)-verbose languages are (h,k)-verbose iff all (m,n)-fa-verbose languages are (h,k)-fa-verbose. In other words, Turing machines and finite automata behave exactly the same way with respect to inclusion of verboseness classes. This identical behaviour implies that the nonspeedup theorem also holds for finite automata. As an application of the theoretical framework, a lower bound is derived on the number of bits that need to be communicated to finite automata protocol checkers for nonregular protocols.

The idea of a finite automaton walking in a labyrinth goes back to Shannon /I/. In the last years this problem has been further investigated by D~pp /2/, M~ller /3/ and Budach /4/. DSpp posed the following question: Does there exist a finite initial automaton that finds a way out of every finite plane open labyrinth from any initial position and finally moves arbitrarily far away ? MGller and Budach gave negative answers to this question, where Budach used DSpp's original definitions, while MGller treated a graph-theoretical variant of D~pp's formulation. It is the aim of this note to show how some quite natural extensions of the computational power of the automaton (called mouse by Shannon) will affect the answer to this question. We allow the mouse to be either a finite automaton, a pushdown transducer, a linear bounded automaton, or a Turing machine. In the first to cases the answer to DSpp's question is negative, while an algorithmic solution for linear bounded automata exists, such that every open labyrinth may be mastered by such mice independent from the starting point. The negative answer in the case of pushdown transducers depends on the fact that there are labyrinths where pushdown transducers have the same computational power as finite automata (which may not master these labyrinths).

Artificial Intelligence (AI) was the inspiration that shaped computing as we know it today. In this article, I explore why and how AI would continue to inspire computing and reinvent it when Moore's Law is running out of steam. At the dawn of computing, Alan Turing proposed that instead of comprising many different specific machines, the computing machinery for AI should be a Universal Digital Computer, modeled after human computers, which carry out calculations with pencil on paper. Based on the belief that a digital computer would be significantly faster, more diligent and patient than a human, he anticipated that AI would be advanced as software. In modern terminology, a universal computer would be designed to understand a language known as an Instruction Set Architecture (ISA), and software would be translated into the ISA. Since then, universal computers have become exponentially faster and more energy efficient through Moore's Law, while software has grown more sophisticated. Even though software has not yet made a machine think, it has been changing how we live fundamentally. The computing revolution started when the software was decoupled from the computing machinery. Since the slowdown of Moore's Law in 2005, the universal computer is no longer improving exponentially in terms of speed and energy efficiency. It has to carry ISA legacy, and cannot be aggressively modified to save energy. Turing's proposition of AI as software is challenged, and the temptation of making many domain-specific AI machines emerges. Thanks to Deep Learning, software can stay decoupled from the computing machinery in the language of linear algebra, which it has in common with supercomputing. A new universal computer for AI understands such language natively to then become a Native Supercomputer. AI has been and will still be the inspiration for computing. The quest to make machines think continues amid the slowdown of Moore's Law. AI might not only maximize the remaining benefits of Moore's Law, but also revive Moore's Law beyond current technology.

The receiver operating characteristic (ROC) curve has been widely applied to classifiers to show how the threshold value for acceptance changes the true positive rate and the false positive rate of the detection jointly. However, it is largely unknown how a biological brain autonomously selects a confidence value for each detection case. In the reported work, we investigated this issue based on the class of Developmental Networks (DNs) which have a power of abstraction similar to symbolic finite automata (FA) but all the DN's representations are emergent (i.e., numeric from the physical world and non-symbolic). Our theory is based on two types of neurotransmitters: Acetylcholine (Ach) and Norepinephrine (NE). Inspired by studies that proposed Ach and NE represent uncertainty and unpredicted uncertainty, respectively, we model how a DN uses Ach and NE to allow neurons to collectively decide acceptance or rejection by estimated novelty based on past experience, instead of using a single threshold value. This is a neural network, distributed, incremental, automatic version of ROC.

Living systems process information using chemistry. Computations can be viewed as language recognition problems where both languages and automata recognizing them form an inclusive hierarchy. Chemical realizations, without using biochemistry, of the main classes of computing automata, Finite Automata (FA), 1-stack Push Down Automata (1-PDA) and Turing Machine (TM) have recently been presented. These use chemistry for the representation of input information, its processing and output information. The Turing machine uses the Belousov-Zhabotinsky (BZ) oscillatory reaction to recognize a representative Context-Sensitive Language (CSL), the 1-PDA uses a pH network to recognize a Context Free Language (CFL) and a FA for a Regular Language (RL) uses a precipitation reaction. By chemically reconfiguring them to recognize representative languages in the lower classes of the Chomsky hierarchy we illustrate the inclusiveness of the hierarchy of native chemical automata. These examples open the door for chemical programming without biochemistry. Furthermore, the thermodynamic metric originally introduced to identify the accept/reject state of the chemical output for the CSL, can equally be used for recognizing CFL and RL by the automata. Finally, we point out how the chemical and thermodynamic duality of accept/reject criteria can be used in the optimization of the energetics and efficiency of computations.

This manuscript contains the experimental realization of one instance of each automata in the theory of computation using chemistry and not using biochemistry. All automata are implemented in a 1-pot reactor. The Finite Automaton (FA) is represented by a precipitation reaction, the 1-stack Push Down Automaton (PDA) by a pH reaction network and the Turing machine (TM) by the Belousov-Zhabotinsky chemical reaction. The computation (consisting on recognizing if chemically transcribed abstract sequences belong to appropriate languages in the Chomsky hierarchy) is carried out by a chemical reaction recognizing the molecules and their order. Once the sequence is introduced in the reactor (very much as mRNA is introduced in the ribosome) the reaction does all the recognition without any need for external not strictly chemical help from reaction/diffusion set-ups or chemical gates. The result of the computation has a straightforward thermodynamic/information theory interpretation. These results are of interest for soft-robotics, chemically self-assembled systems, chemical neural networks, artificial intelligence and of course chemical computing (i. e., computing done by chemistry at molecular scales which translates to larger scales by the power of Avogadro's number) as well as natural computing and analog/digital computing.

A number of authors have used formal models of computation to capture the idea of “bounded rationality” in repeated games. Most of this literature has used computability by a finite automaton as the standard. A conceptual difficulty with this standard is that the decision problem is not “closed.” That is, for every strategy implementable by an automaton, there is some best response implementable by an automaton, but there may not exist any algorithm forfinding such a best response that can be implemented by an automaton. However, such algorithms can always be implemented by a Turing machine, the most powerful formal model of computation. In this paper, we investigate whether the decision problem can be closed by adopting Turing machines as the standard of computability. The answer we offer is negative. Indeed, for a large class of discounted repeated games (including the repeated Prisoner's Dilemma) there exist strategies implementable by a Turing machine for whichno best response is implementable by a Turing machine.

The main thesis of this chapter is that a dynamical viewpoint allows us to better understand some important foundational issues of computation theory. Effective procedures are traditionally studied from two different but complementary points of view. The first approach is concerned with individuating those numeric functions that are effectively calculable. This approach reached its systematization with the theory of the recursive functions (Gödel, Church Kleene).This theory is not directly concerned with computing devices or computations. Rather, the effective calculability of a recursive function is guaranteed by the algorithmic nature of its definition. In contrast, the second approach focuses on a family of abstract mechanisms, which are then typically used to compute or recognize numeric functions, sets of numbers, or numbers. These devices can be divided into two broad categories: automata or machines (Turing and Post), and systems of rules for symbol manipulation (Post). The mechanisms that have been studied include: a. Automata or Machines 1. gate-nets and McCulloch-Pitts nets 2. finite automata (Mealy and Moore machines) 3. push-down automata 4. stack automata 5. Turing machines 6. register machines 7. wang machines 8. cellular automata b. Systems of Rules 9. monogenic production systems in general 10. monogenic Post canonical systems 11. monogenic Post normal systems 12. tag systems. I call any device studied by computation theory a computational system. Computation theory is traditionally interested in studying the relations between each type of computational system and the others, and in establishing what class of numeric functions each type can compute. Accordingly one proves two kinds of theorem: (1) that systems of a given type emulate systems of another type (examples: Turing machines emulate register machines and cellular automata; cellular automata emulate Turing machines, etc.), and (2) that a certain type of system is complete relative to the class of the (partial) recursive functions or, in other words, that this type of system can compute all and only the (partial) recursive functions (examples of complete systems: Turing machines, register machines, cellular automata, tag systems, etc.). All different types of computational systems have much in common. Nevertheless, it is not at all clear exactly which properties these mechanisms share.

Bounded rationality aims to understand the effects of how limited rationality affects decision-making. The traditional models in game theory and multiagent system research, such as finite automata or unrestricted Turing machine, fall short of capturing how intelligent agents make decision in realistic applications. To address this problem, we model bounded rational agents as restricted Turing machines: restrictions on running time and on storage space. We then study our model in two-person repeated games. In the case where the running time of Turing machines is restricted, we show that computing the best response of a given strategy is much harder than the strategy itself. In the case where the storage space of the Turing machines is restricted, we show the best response of a space restricted strategy can not be implemented by machines within the same size (up to a constant factor). Finally, we study how these restrictions affect the set of Nash equilibria in infinitely repeated games. We show restricting the agent's computational resources will give rise to new Nash equilibria.

Bounded rationality aims to understand the effects of how limited rationality affects decision-making. The traditional models in game theory and multiagent system research, such as finite automata or unrestricted Turing machine, fall short of capturing how intelligent agents make decision in realistic applications. To address this problem, we model bounded rational agents as restricted Turing machines: restrictions on running time and on storage space. We study our model under the context of two-person repeated games. In the case where the running time of Turing machines is restricted, we show that computing the best response of a given strategy is much harder than the strategy itself. In the case where the storage space of the Turing machines is restricted, we show the best response of a space restricted strategy can not be implemented by machines within the same size (up to a constant factor). Finally, we study how these restrictions affect the set of Nash equilibria in infinitely repeated games.We show restricting the agent’s computational resources will give rise to new Nash equilibria.

BackgroundIn response to recent real world events impacting public health and medical services, The Yale New Have Center for Emergency Preparedness and Disaster Response (YNH-CEPDR) has developed a methodology for collection and analysis for after action reporting of response operation effectiveness. This process has been implemented to multiple real-world events including the 2009/2010 H1N1 response activities. This method utilizes the US Department of Homeland Security Exercise and Evaluation Program (HSEEP) doctrine for the collection of response information, analysis and development of After Action Reports.ObjectivesIn this session, participants will be introduced to data collection methods that include a combination of onsite response evaluation by subject matter experts applying a set of established operational response objectives, targeted web-based surveys collecting both qualitative and quantitative data regarding public health and medical staff opinions regarding response operations and achievement of objectives. Also introduced will be focus group interviews to determine response successes, opportunities and recommendations for improvement. This session will also provide an overview on the utilization of additional data sources including situational status reports, press releases, incident action plans and meeting minutes. In additional to providing a framework for developing a comprehensive After Action Report for a real-world response, this process can yield data that can be used to enhance ongoing response operations as well as to support anticipated response operations, such as applying lessons from one pandemic wave to the next. During the session, participants will be provided an opportunity to discuss their process for evaluating real-world events and to identify how this methodology can be integrated into their organization's response evaluation activities.

In this paper we present the new version of a tool to assist in teaching formal languages and automata theory. In the previous version the tool provided algorithms for regular expressions, finite automata and context free grammars. The new version can simulate as well push-down automata and Turing machines.

Finite devices accepting infinite strings are the topic of several papers (see the recent surveys [4], [8] or [10], [11]). Most of these papers deal with finite automata. Thus finite automata as devices accepting infinite strings are wellunderstood. The situation is a little bit more involved if one considers more complicated accepting devices like, e.g., pushdown automata or Turing machines.

A Rice-style theorem for parallel automata

The use of blogs to track and comment on real world (political, news, entertainment) events is growing. Similarly, as more individuals start relying on the Web as their primary information source and as more traditional media outlets try reaching consumers through alternative venues, the number of news sites on the Web is also continuously increasing. Content-reuse, whether in the form of extensive quotations or content borrowing across media outlets, is very common in blogs and news entries outlets tracking the same real-world event. Knowledge about which web entries re-use content from which others can be an effective asset when organizing these entries for presentation. On the other hand, this knowledge is not cheap to acquire: considering the size of the related space web entries, it is essential that the techniques developed for identifying re-use are fast and scalable. Furthermore, the dynamic nature of blog and news entries necessitates incremental processing for reuse detection. In this paper, we develop a novel qSign algorithm that efficiently and effectively analyze the blogosphere for quotation and reuse identification. Experiment results show that with qSign processing time gains from 10X to 100X are possible while maintaining reuse detection rates of upto 90%. Furthermore, processing time gains can be pushed multiple orders of magnitude (from 100X to 1000X) for 70% recall.