Ans.
Water Jugs Problem

• Water jugs problem: We have one 3 litre jug, one 5 litre jug and an unlimited supply of water. The goal is to get exactly one litre of water into either jug. Either jug can be emptied or filled, or poured into the other.
  
  
  
• A state in this problem could be represented with just a pair of numbers. The first representing the number of litres of water in the 5 litre (large) jug, and the second representing the number of litres of water in the 3 litre (small) jug.
• The initial state would typically be: (0,0) to represent the fact that both jugs start off empty.
• The final state would similarly be represented as: (0,1).
• The operators for this problem could include:
  1) Fill the 5 litre jug to capacity from a water source
  2) Fill the 3 litre jug to capacity from a water source
  3) Empty the 5 litre jug into a drain
  4) Empty the 3 litre jug into a drain
  5) Pour from the 3 litre jug into 5 litre jug until capacity reached
  6) Pour from the 3 litre jug into 5 litre jug until capacity reached

Traveling Salesman Problem

Starting at A, find the shortest path through all the cities, visiting each city exactly once and returning to A.

ANS.
"A physical symbol system has the necessary and sufficient means for intelligent action."

A physical symbol system "consists of a set of entities, called symbols, which are physical patterns that can occur as components of another type of entity called an expression (or symbol structure). Thus, a symbol structure is composed of a number of instances (or tokens) of symbols related in some physical way (such as one token being next to another). At any instant of time the system will contain a collection of these symbol structures. Besides these structures, the system also contains a collection of processes that operate on expressions to produce other expressions: processes of creation, modification, reproduction and destruction. A physical symbol system is a machine that produces through time an evolving collection of symbol structures. Such a system exists in a world of objects wider than just these symbolic expressions themselves."

"Two notions are central to this structure of expressions, symbols, and objects: designation and interpretation."

"Designation. An expression designates an object if, given the expression, the system can either affect the object itself or behave in ways dependent on the object. ... In either case, access to the object via the expression has been obtained, which is the essence of designation."

"Interpretation. The system can interpret an expression if the expression designates a process and if, given the expression, the system can carry out the process. ...Interpretation implies a special form of dependent action: given an expression the system can perform the indicated process, which is to say, it can evoke and execute its own processes from expressions that designate them."