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1. The central question of <computability, complexity, automata> theory is What

ID: 3616779 • Letter: 1

Question

1.                     The central question of <computability, complexity, automata> theory is What makes some problems difficult and others easy?

2.                     The central question of <computability, complexity, automata> theory is What problems are theoretically solvable?

3.                     Some problems cannot be solved by computers.

4.                     <one or two of computability, complexity, automata> theory require precise definitions of computers and computation, which are provided by <computability, complexity, automata> theory.

5.                     <a set> = <a set>

6.                     <a set> Í <a set>

7.                     {} Í <a set>

8.                     <a sequence> = <a sequence>

9.                     A <some integer>-tuple is also called a binary sequence.

10.                A <some integer>-tuple is also called an ordered pair.

11.                <sets, sequences> may be elements of <sets, sequences>.

12.                The <domain, range> of a function can be a cross-product.

13.                The set of possible “inputs” to a function is called its <range, domain>.

14.                The <input, output> of a function is called an argument.

15.                A function is <into, onto> if there are some values in the <domain, range> for which the function is not defined.

16.                A function is <one-to-one, many-to-one> if every value in the <domain, range> maps to only one value in the <domain, range>.

17.                The relation <a common algebraic relation such as equal, greater than, less than, greater than or equal, less than or equal, not equal> over the real numbers is <reflexive, symmetric, transitive>.

18.                In <a directed, an undirected> graph, there can only be one path between any two nodes.

19.                A labeled graph may have labeled <edges, nodes>.

20.                A tree is a <description of some kind of graph>.

21.                For strings w and v, wv = <some combination of v, w, and e>.

22.                ee = e.

23.                <some set or sequence specification> is a language.

24.                With just <some Boolean operation> the equivalent of all Boolean operations can performed.

Short Answer

25. Which area of computer science theory deals with mathematical models of computation?

26. Using <the ellipsis, a rule, enumeration>, what is the mathematical definition of the set <English description of a set>?

27. Use <the ellipsis, a rule, enumeration> to give the definition of the set <a set described with the ellipsis, a rule, enumeration>.

28. What is the cardinality of the set <a set described in English or with the ellipsis, a rule, enumeration>?

29. Use <the ellipsis, a rule, enumeration> to give the set <sets specified with the union, intersection or cross product operator>.

30. Use <the ellipsis, a rule, enumeration> to give the power set of <a finite set described in English or with the ellipsis, a rule, enumeration>.

31. Use <the ellipsis, a rule, enumeration> to give the set < a set described with the ellipsis, a rule, or enumeration that is followed by a superscript; i.e. {1,a}4>.

32. For X = <a finite set> and Y = <another finite set>, which of the following are a functions from X to Y < The corresponding values of X and Y will be shown in tabular form as in the example below. NB: other variables than X and Y may be used for the sets>? Which are one-to-one? Which are onto?

X

Y

g

3

h

4

                        .

                        .

                        .

33. What is another term for a mapping?

34. What is a binary function?

35. What is the <range, domain> for a predicate?

36. For relation R, what does aRb signify?

37. For a set <some set specified by enumeration, ellipsis, or rule; e.g.{a, b, c}> and a relation on it such that <a relation specified using infix notation; e.g. aRb and so forth> is R <reflexive, symmetric, transitive>?

38. For graph G = <specified mathematically> and graph H = <specified mathematically>, is H a subgraph of G?

39. 

X

Y

g

3

h

4

Explanation / Answer

1.     False Thecentral question of <computability, complexity, automata>theory is What makes some problems difficult and others easy?

2.      True Thecentral question of <computability, complexity, automata>theory is What problems are theoretically solvable?

3.       True  Some problems cannot be solved by computers.

4.       true  <one or two of computability, complexity, automata> theoryrequire precise definitions of computers and computation, which areprovided by <computability, complexity, automata> theory.

5.              True     <a set> = <a set>

6.               Symbolis not undersatandable     <aset> Í <a set>

7.                   {} Í <a set>

8.              true  <a sequence> = <a sequence>

9.         False          A <some integer>-tuple is also called a binarysequence.

10.        true       A <some integer>-tuple is also called an orderedpair.

11.      true         <sets, sequences> may be elements of <sets,sequences>.

12.     true          The <domain, range> of a function can be across-product.

13.       true        The set of possible “inputs” to a functionis called its <range, domain>.

14.           false    The <input, output> of a function is called anargument.

15.        true       A function is <into, onto> if there are some valuesin the <domain, range> for which the function is notdefined.

16.        true       A function is <one-to-one, many-to-one> if every value in the<domain, range> maps to only one value in the <domain,range>.

17.          false    The relation <a common algebraic relation such as equal, greaterthan, less than, greater than or equal, less than or equal, notequal> over the real numbers is <reflexive, symmetric,transitive>.

18.         false      In <a directed, an undirected> graph, there canonly be one path between any two nodes.

19.         true      A labeled graph may have labeled <edges,nodes>.

20.         true      A tree is a <description of some kind ofgraph>.

21.          true     For strings w and v, wv = <some combination of v, w, ande>.

22.          false     ee = e.

23.          true     <some set or sequence specification> is alanguage.

24.          true     With just <some Boolean operation> theequivalent of all Boolean operations can performed.