1. Supplement Beyond Computation
CIS 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