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Supplement Beyond Computation

Delve into the origins, theories, and controversies surrounding automata, formal languages, and computational paradigms, including Chomsky's Hierarchy and the quest for Artificial General Intelligence. Explore beyond Turing computation with various models and perspectives. Understand the intersection of intelligence and computation in problem-solving scenarios.

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Supplement Beyond Computation

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  1. SupplementBeyond Computation CIS 5513 - Automata and Formal Languages – Pei Wang

  2. The study of automata This research started in mathematics as attempts to define notions like computable function, effective procedure, algorithm, etc. Later, this work was related to formal language, and resulted in the theory of computation Further developments in various directions: • Cellular automata • Probabilistic automata

  3. The study of formal languages The Chomsky school in linguistics assumes human innate linguistic competence in the form of formal grammars The Chomsky Hierarchy systematically summarizes the relations among formal languages and computational models A more comprehensive list includes other formal languages (e.g., the grammar for {anbncn| n ≥ 1}) and automata

  4. The computation paradigm Basic approach: • To specify a problem as a function • To specify a solution as an algorithm Possibilities: • The function is uncomputable • The function is computable (decidable, recursive) then computational complexity is the issue

  5. Controversial issues • Can natural languages be analyzed as formal languages? • Can thinking be analyzed as computing? • Can mind be analyzed as computer? There are different beliefs: • Yes, if we work harder • No, they are fundamentally different • Yes, if we use non-traditional models

  6. Models that are not TM-equivalent There have been various attempts to go beyond the conceptual framework of Turing computation: • Trial-and-error procedures • Anytime algorithms • Interactive computation • Analog computers • Hypercomputation

  7. Computation as a perspective TM is not a device, but a program or a process in a device, so it is a particular way to analyze and to use a computational device It is possible for some processes in an ordinary computer to be beyond computation Computation and Intelligence in Problem Solving discusses such a possibility in a system (NARS) toward Artificial General Intelligence

  8. Problem solving in NARS • NARS has a constant number of basic operations, each does a certain computation • NARS accepts tasks at any time with any expressible content and time requirement • NARS uses its available knowledge and resources on each task to achieve the best-possible result • NARS learns new knowledge constantly • NARS dynamically allocates its resources

  9. Intelligence vs. computation • An ordinary problem is an instance, not a set • Time requirement is often part of a problem • A solution’s quality is a matter of degree • A problem may get any number of solution • A system never returns to an earlier state • Intelligent problem solving is adaptive, creative, flexible, and case-by-case, though neither predictable nor repeatable

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