Non-computable strategies and discounted repeated games

It has been shown that a Developmental Network (DN) can learn any Finite Automaton (FA) [29] but FA is not a general purpose automaton by itself. This theoretical paper presents that the controller of any Turing Machine (TM) is equivalent to an FA. It further models a motivation-free brain — excluding motivation e.g., emotions — as a TM inside a grounded DN — DN with the real world. Unlike a traditional TM, the TM-in-DN uses natural encoding of input and output and uses emergent internal representations. In Artificial Intelligence (AI) there are two major schools, symbolism and connectionism. The theoretical result here implies that the connectionist school is at least as powerful as the symbolic school also in terms of the general-purpose nature of TM. Furthermore, any TM simulated by the DN is grounded and uses natural encoding so that the DN autonomously learns any TM directly from natural world without a need for a human to encode its input and output. This opens the door for the DN to fully autonomously learn any TM, from a human teacher, reading a book, or real world events. The motivated version of DN [31] further enables a DN to go beyond action-supervised learning — so as to learn based on pain-avoidance, pleasure seeking, and novelty seeking [31].

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).

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.

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.

This paper presents HyperFlow: an approach to workflow programming which combines the advantages of a declarative workflow description and low-level scripting programming. The workflow execution model of HyperFlow is based on a formal model of computation - Process Networks. The execution environment is implemented on the basis of a widely adopted runtime platform node.js. Workflow programming benefits from such an approach in multiple ways, including leveraging a large programming ecosystem with many developers, reusable software packages and learning resources; elimination of shim nodes from the workflow graph; and increased reusability of workflow processing components. The HyperFlow workflow programming approach and its advanced capabilities are presented. The HyperFlow engine is also briefly described. Four example workflow applications from various domains, including flood threat assessment, are studied as a demonstration of the HyperFlow programming approach and a comparison with related solutions.

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.

The Panopticon (which means “watcher of everything”) is a well-known prison structure of continuous surveillance and discipline studied by Bentham in 1785. Today, where persistent, massive scale, surveillance is immensely facilitated by new technologies, the term Panopticon vaguely characterizes institutions with a power to acquire and process, undetectably, personal information. In this paper we propose a theoretical framework for studying Panopticons and their detectability status. We show, based on the Theory of Computation, that detecting Panopticons, modelled either as a simple Turing Machine or as an Oracle Turing Machine, is an undecidable problem. Furthermore, we show that for each sufficiently expressive formal system, we can effectively construct a Turing Machine for which it is impossible to prove, within the formal system, its Panopticon status. Finally, we discuss how Panopticons can be physically detected by the heat they dissipate each time they acquire, effortlessly, information in the form of an oracle and we investigate their detectability status with respect to a more powerful computational model than classical Turing Machines, the Infinite Time Turing Machines (ITTMs).

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

CHAPTER 2 - A Catalog of Complexity Classes

Classes of discrete optimization problems and their decision problems

The Turing machine convincingly formalized the concepts of “algorithm,” “computation,” and “computable.” It convinced researchers by its simplicity, generality, mechanical operation, and resemblance to human activity when solving computational problems, and by Turing’s reasoning and analysis of “computable” functions and his argumentation that partial “computable” functions are exactly Turing computable functions. Turing considered several variants that are generalizations of the basic model of his machine. But he also proved that they add nothing to the computational power of the basic model. This strengthened the belief in the Turing machine as an appropriate model of computation. Turing machines can be encoded and consequently enumerated. This enabled the construction of the universal Turing machine that is capable of computing anything that can be computed by any other Turing machine. This seminal discovery laid the theoretical grounds for several all important practical consequences, the general-purpose computer and the operating system being the most notable. The Turing machine is a versatile model of computation: it can be used to compute values of a function, or to generate elements of a set, or to decide about the membership of an object in a set. The last led to the notions of decidable and semi-decidable sets that would later prove to be very important in solving general computational problems.