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