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COMPSCI4009 Algorithmics I (H) 2025-26

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Does nondeterminism increase the languages that can be expressed

by pushdown automata?

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Does nondeterminism increase the languages that can be expressed

by finite state automata?

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Which of the following can be computed by a deterministic finite

state automaton? (Select all that are computable)?

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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.
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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.

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

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

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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?

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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?

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In a topological ordering is it always the case that, if v is a sink, then it true that lab(u) < lab(v) for all non-sink vertices u
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