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COMPSCI4009 Algorithmics I (H) 2025-26

COMPSCI4009 Algorithmics I (H) 2025-26

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Does nondeterminism increase the languages that can be expressed

by pushdown automata?

Does nondeterminism increase the languages that can be expressed

by finite state automata?

Which of the following can be computed by a deterministic finite

state automaton? (Select all that are computable)?

Strings which have no single as (i.e. any a is either preceded or followed by another a).

✅

Strings that start and end with the same character.

Strings which have more as than bs.

Strings that start with a certain number of as end with the same number of as.

❌

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Over the alphabet {a,b}, which of the following the regular

expressions represents the language which consists of

all the strings that

start and end with different symbols.

b(a|b)^*a

(a(a|b)^*b) | (b(a|b)^*a)

a(a|b)^*b

All of the above.

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Over the alphabet {a,b}

, which of the following the regular

expressions represents the language which consists of

all

the strings that

starts with

ab and ends with ba.

aba^*b^*ba

ab(ab)^*ba

ab(a|b)^*ba

Which of the following strings is a member of the language over {a,b} defined by the regular expression (aa|ba)^*(bb)^*?

aaaabb

babbaa

bbaa

aabbba

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Suppose problem X is NP-complete, problem Y is in class NP, and there is a polynomial reduction from X to Y. Which of the following is true?

None of the above.

❌

Problem Y is in class P.

❌

Both of the above.

❌

Problem Y is NP–complete.

✅

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Suppose problem X is NP-complete, problem Y is in class P, and there is polynomial reduction from X to Y. If Z is NP-complete, which of the following is true?